Homework answers / question archive / 1) In statistics, what does df denote? If a simple random sample of 18 speeds of cars on California Highway 405 is to be used to test the claim that the sample values are from a population with a mean greater than the posted speed limit of 65 mi/h, what is the specific value of df? Choose the correct answer below

1) In statistics, what does df denote? If a simple random sample of 18 speeds of cars on California Highway 405 is to be used to test the claim that the sample values are from a population with a mean greater than the posted speed limit of 65 mi/h, what is the specific value of df? Choose the correct answer below

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1) In statistics, what does df denote? If a simple random sample of 18 speeds of cars on California Highway 405 is to be used to test the claim that the sample values are from a population with a mean greater than the posted speed limit of 65 mi/h, what is the specific value of df?

Choose the correct answer below.

A. df denotes the distribution of freedom. For this sample, df= 18.

B. df denotes the number of degrees of freedom. For this sample, df= 17.

C. df denotes the number of degrees of freedom. For this sample, df= 18.

D. df denotes the distribution of freedom. For this sample, df= 17.

2. Use technology to find the P-value for a right-tailed test about a mean with n = 22 and test statistic t = 1.263.

P-value » 0.1102 (Round to four decimal places as needed. )

YOU ANSWERED: .7870

3. Using a table of critical t-values of the t distribution, find the range of values for the P-value for testing a claim about the mean body temperature of healthy adults for a left-tailed test with n = 13 and test statistic t= - 2.428.

¹Click the icon to view a table of critical t-values.

What is the range of values for the P-value?

A. P-value < 0.005

B. 0.01<P-value < 0.025

C. 0.005 < P-value < 0.01

D. 0.025 < P-value <0.05

1: t-table

t distribution: Critical t values

	Area in One Tall 0.005                        0.01                       0.025                        0.05                   0.10
Degrees of Freedom	Area in Two Tails 0.01                          0.02                       0.05                       0.10                          0.20
1	63.657	31.821	12.706	6.314	3.078
2	9.925	6.965	4.303	2.920	1.886
3	5.841	4.541	3.182	2.353	1.638
4	4.604	3.747	2.776	2.132	1.533
5	4.032	3.365	2.571	2.015	1.476
6	3.707	3.143	2.447	1.943	1.440
7	3.499	2.998	2.365	1.985	1.415
8	3.355	2.896	2.306	1.860	1.397
9	3.250	2.821	2.262	1.833	1.383
10	3.169	2.764	2.228	1.812	1.372
11	3.106	2.718	2.201	1.796	1.363
12	3.055	2.681	2.179	1.782	1.356
13	3.012	2.650	2.160	1.771	1.350
14	2.977	2.624	2.145	1.761	1.345
15	2.947	2.602	2.131	1.753	1.341
16	2.921	2.583	2.120	1.746	1.337
17	2.898	2.567	2.110	1.740	1.333
18	2.878	2.552	2.101	1.734	1.330
19	2.861	2.539	2.093	1.729	1.328
20	2.845	2.528	2.086	1.725	1.325
21	2.831	2.518	2.080	1.721	1.323
22	2.819	2.508	2.074	1.717	1.321
23	2.807	2.500	2.069	1.714	1.319
24	2.797	2.492	2.064	1.711	1.318
25	2.787	2.485	2.060	1.708	1.316
26	2.779	2.479	2.056	1.706	1.315
27	2.771	2.473	2.052	1.703	1.314
28	2.763	2.467	2.048	1.701	1.313
29	2.756	2.462	2.045	1.699	1.311
30	2.750	2.457	2.042	1.697	1.310
31	2.744	2.453	2.040	1.696	1.309
32	2.738	2.449	2.037	1.694	1.309
33	2.733	2.445	2.035	1.692	1.308
34	2.728	2.441	2.032	1.691	1.307
35	2.724	2.438	2.030	1.690	1.306
36	2.719	2.434	2.028	1.688	1.306
37	2.715	2.431	2.026	1.687	1.305
38	2.712	2.429	2.024	1.686	1.304
39	2.708	2.426	2.023	1.685	1.304
40	2.704	2.423	2.021	1.684	1.303
45	2.690	2.412	2.014	1.679	1.301
50	2.678	2.403	2.009	1.676	1.299
60	2.660	2.390	2.000	1.671	1.296
70	2.648	2.381	1.994	1.667	1.294
80	2.639	2.374	1.990	1.664	1.292
90	2.632	2.368	1.987	1.662	1.291
100	2.626	2.364	1.984	1.660	1.290
200	2.601	2.345	1.972	1.653	1.286
300	2.592	2.339	1.968	1.650	1.284
400	2.588	2.336	1.966	1.649	1.284
500	2.586	2.334	1.965	1.648	1.283
1000	2.581	2.330	1.962	1.646	1.282
2000	2.578	2.328	1.961	1.646	1.282
Large	2.576	2.326	1.960	1.645	1.282
Degrees of Freedom	Area in One Tail 0.005                       0.01                        0.025                       0.05                      0.10
	Area in Two Tails 0.01                         0.02                        0.05                           0.10                     0.20

 

YOU ANSWERED: A.

4. Using a table of critical t-values of the t distribution, find the range of values for the P-value for a two-tailed test with n=1/7 and test statistic t= 1.899.

²Click the icon to view a table of critical t-values.

What is the range of values for the P-value?

A. 0.05<P-value <0.10

B. 0.10<P-value <0.20

C. 0.01 < P-value <0.02

D. 0.025 <P-value <0.05

2: t-table

t distribution: Critical t values

	Area in One Tall 0.005                        0.01                       0.025                        0.05                   0.10
Degrees of Freedom	Area in Two Tails 0.01                          0.02                       0.05                       0.10                          0.20
1	63.657	31.821	12.706	6.314	3.078
2	9.925	6.965	4.303	2.920	1.886
3	5.841	4.541	3.182	2.353	1.638
4	4.604	3.747	2.776	2.132	1.533
5	4.032	3.365	2.571	2.015	1.476
6	3.707	3.143	2.447	1.943	1.440
7	3.499	2.998	2.365	1.985	1.415
8	3.355	2.896	2.306	1.860	1.397
9	3.250	2.821	2.262	1.833	1.383
10	3.169	2.764	2.228	1.812	1.372
11	3.106	2.718	2.201	1.796	1.363
12	3.055	2.681	2.179	1.782	1.356
13	3.012	2.650	2.160	1.771	1.350
14	2.977	2.624	2.145	1.761	1.345
15	2.947	2.602	2.131	1.753	1.341
16	2.921	2.583	2.120	1.746	1.337
17	2.898	2.567	2.110	1.740	1.333
18	2.878	2.552	2.101	1.734	1.330
19	2.861	2.539	2.093	1.729	1.328
20	2.845	2.528	2.086	1.725	1.325
21	2.831	2.518	2.080	1.721	1.323
22	2.819	2.508	2.074	1.717	1.321
23	2.807	2.500	2.069	1.714	1.319
24	2.797	2.492	2.064	1.711	1.318
25	2.787	2.485	2.060	1.708	1.316
26	2.779	2.479	2.056	1.706	1.315
27	2.771	2.473	2.052	1.703	1.314
28	2.763	2.467	2.048	1.701	1.313
29	2.756	2.462	2.045	1.699	1.311
30	2.750	2.457	2.042	1.697	1.310
31	2.744	2.453	2.040	1.696	1.309
32	2.738	2.449	2.037	1.694	1.309
33	2.733	2.445	2.035	1.692	1.308
34	2.728	2.441	2.032	1.691	1.307
35	2.724	2.438	2.030	1.690	1.306
36	2.719	2.434	2.028	1.688	1.306
37	2.715	2.431	2.026	1.687	1.305
38	2.712	2.429	2.024	1.686	1.304
39	2.708	2.426	2.023	1.685	1.304
40	2.704	2.423	2.021	1.684	1.303
45	2.690	2.412	2.014	1.679	1.301
50	2.678	2.403	2.009	1.676	1.299
60	2.660	2.390	2.000	1.671	1.296
70	2.648	2.381	1.994	1.667	1.294
80	2.639	2.374	1.990	1.664	1.292
90	2.632	2.368	1.987	1.662	1.291
100	2.626	2.364	1.984	1.660	1.290
200	2.601	2.345	1.972	1.653	1.286
300	2.592	2.339	1.968	1.650	1.284
400	2.588	2.336	1.966	1.649	1.284
500	2.586	2.334	1.965	1.648	1.283
1000	2.581	2.330	1.962	1.646	1.282
2000	2.578	2.328	1.961	1.646	1.282
Large	2.576	2.326	1.960	1.645	1.282
Degrees of Freedom	Area in One Tail 0.005                       0.01                        0.025                       0.05                      0.10
	Area in Two Tails 0.01                         0.02                        0.05                           0.10                     0.20

 

YOU ANSWERED: D.

5. Assume that a simple random sample has been selected and test the given claim. Use the P-value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

The ages of actresses when they won an acting award is summarized by the statistics n = 78, x = 35.8 years, and s = 11.7 years. Use a 0.05 significance level to test the claim that the mean age of actresses when they win an acting award is 32 years.

What are the hypotheses?

A. H₀: m = 32 years

     H₁: m ³ 32 years

B. H₀: m ¹ 32 years

     H₁: m = 32 years

C. H₀: m = 32 years

    H₁: m < 32 years

D. H₀: m = 32 years

   H₁: m ¹ 32 years

Identify the test statistic.

t= __________________ (Round to three decimal places as needed. )

Identify the P-value.

The P-value is _____________________ (Round to four decimal places as needed.)

State the final conclusion that addresses the original claim. Choose the correct answer below.

A. Fail to reject H₀. There is sufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 32 years.

B. Reject H₀. There is sufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 32 years.

C. Fail to reject H₀. There is insufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 32 years.

D. Reject H₀. There is insufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 32 years.

6. Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

A simple random sample of 25 filtered 100 mm cigarettes is obtained, and the tar content of each cigarette is measured. The sample has a mean of 19.2 mg and a standard deviation of 3.56 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg, which is the mean for unfiltered king size cigarettes. What do the results suggest, if anything, about the effectiveness of the filters?

What are the hypotheses?

A. H₀: m < 21.1 mg

     H₁: m ³ 21.1 mg

B. H₀: m > 21.1 mg

     H₁: m < 21.1 mg

C. H₀: m = 21.1 mg

    H₁: m < 21.1 mg

D. H₀: m = 21.1 mg

   H₁: m ³ 21.1 mg

Identify the test statistic.

t=__________________________ (Round to three decimal places as needed. )

Identify the P-value.

The P-value is _______________________________________

(Round to four decimal places as needed. )

State the final conclusion that addresses the original claim. Choose the correct answer below.

A. Fail to reject H₀. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

B. Fail to reject H₀. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

C. Reject H₀. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

D. Reject H₀. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

What do the results suggest, if anything, about the effectiveness of the filters?

A. The results do not suggest that the filters are effective.

B. The results suggest that the filtered cigarettes have the same tar content as unfiltered king size cigarettes.

C. The results are inconclusive because the sample size is less than 30.

D. The results suggest that the filters are effective.

E. The results suggest that the filters increase the tar content.

7. For the following claim, find the null and alternative hypotheses, test statistic, critical value, and draw a conclusion.

Assume that a simple random sample has been selected from a normally distributed population. Answer parts a-d.

Claim: The mean IQ score of statistics professors is less than 133.

Sample data: n= 11, x=130, s=2. The significance level is a =0.05.

³Click the icon to view a table of critical t-values.

a. Choose the correct null hypothesis (H₀) and alternative hypothesis (H₁).

A. H₀: m = 133               H₁: m ¹ 133

B. H₀: m < 133               H₁: m = 133

C. H₀: m < 133               H₁: m > 133

D. H₀: m = 133              H₁: m < 133

b. Determine the test statistic t.

t= _____________________________ (Round to three decimal places as needed. )

c. Find the critical value using a t-distribution table.

The critical value is __________________ . (Round to three decimal places as needed.)

d. What is the conclusion?

A. Fail to reject the null hypothesis and support the claim that m < 133.

B. Fail to reject the null hypothesis and do not support the claim that m < 133.

C. Reject the null hypothesis and do not support the claim that m < 133.

D. Reject the null hypothesis and support the claim that m < 133.

3: t-table

t distribution: Critical t values

	Area in One Tall 0.005                        0.01                       0.025                        0.05                   0.10
Degrees of Freedom	Area in Two Tails 0.01                          0.02                       0.05                       0.10                          0.20
1	63.657	31.821	12.706	6.314	3.078
2	9.925	6.965	4.303	2.920	1.886
3	5.841	4.541	3.182	2.353	1.638
4	4.604	3.747	2.776	2.132	1.533
5	4.032	3.365	2.571	2.015	1.476
6	3.707	3.143	2.447	1.943	1.440
7	3.499	2.998	2.365	1.985	1.415
8	3.355	2.896	2.306	1.860	1.397
9	3.250	2.821	2.262	1.833	1.383
10	3.169	2.764	2.228	1.812	1.372
11	3.106	2.718	2.201	1.796	1.363
12	3.055	2.681	2.179	1.782	1.356
13	3.012	2.650	2.160	1.771	1.350
14	2.977	2.624	2.145	1.761	1.345
15	2.947	2.602	2.131	1.753	1.341
16	2.921	2.583	2.120	1.746	1.337
17	2.898	2.567	2.110	1.740	1.333
18	2.878	2.552	2.101	1.734	1.330
19	2.861	2.539	2.093	1.729	1.328
20	2.845	2.528	2.086	1.725	1.325
21	2.831	2.518	2.080	1.721	1.323
22	2.819	2.508	2.074	1.717	1.321
23	2.807	2.500	2.069	1.714	1.319
24	2.797	2.492	2.064	1.711	1.318
25	2.787	2.485	2.060	1.708	1.316
26	2.779	2.479	2.056	1.706	1.315
27	2.771	2.473	2.052	1.703	1.314
28	2.763	2.467	2.048	1.701	1.313
29	2.756	2.462	2.045	1.699	1.311
30	2.750	2.457	2.042	1.697	1.310
31	2.744	2.453	2.040	1.696	1.309
32	2.738	2.449	2.037	1.694	1.309
33	2.733	2.445	2.035	1.692	1.308
34	2.728	2.441	2.032	1.691	1.307
35	2.724	2.438	2.030	1.690	1.306
36	2.719	2.434	2.028	1.688	1.306
37	2.715	2.431	2.026	1.687	1.305
38	2.712	2.429	2.024	1.686	1.304
39	2.708	2.426	2.023	1.685	1.304
40	2.704	2.423	2.021	1.684	1.303
45	2.690	2.412	2.014	1.679	1.301
50	2.678	2.403	2.009	1.676	1.299
60	2.660	2.390	2.000	1.671	1.296
70	2.648	2.381	1.994	1.667	1.294
80	2.639	2.374	1.990	1.664	1.292
90	2.632	2.368	1.987	1.662	1.291
100	2.626	2.364	1.984	1.660	1.290
200	2.601	2.345	1.972	1.653	1.286
300	2.592	2.339	1.968	1.650	1.284
400	2.588	2.336	1.966	1.649	1.284
500	2.586	2.334	1.965	1.648	1.283
1000	2.581	2.330	1.962	1.646	1.282
2000	2.578	2.328	1.961	1.646	1.282
Large	2.576	2.326	1.960	1.645	1.282
Degrees of Freedom	Area in One Tail 0.005                       0.01                        0.025                       0.05                      0.10
	Area in Two Tails 0.01                         0.02                        0.05                           0.10                     0.20

 

8. Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

A safety administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in hic (standard head injury condition units). The safety requirement is that the hic measurement should be less than 1000 hic. Use a 0.05 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified requirement?

     635            665            1150             613                 532                 575

What are the hypotheses?

A. H₀: m < 1000 hic

     H₁: m ³ 1000 hic

B. H₀: m = 1000 hic

     H₁: m < 1000 hic

C. H₀: m > 1000 hic

    H₁: m < 1000 hic

D. H₀: m = 1000 hic

   H₁: m ³ 1000 hic

Identify the test statistic.

t= ____________________ (Round to three decimal places as needed. )

Identify the P-value.

The P-value is ___________________.

(Round to four decimal places as needed. )

State the final conclusion that addresses the original claim.

(1) _______ H₀. There is (2) ________ evidence to support the claim that the sample is from a population with a mean less than 1000 hic.

What do the results suggest about the child booster seats meeting the specified requirement?

A. There is strong evidence that the mean is less than 1000 hic, but one of the booster seats has a measurement that is greater than 1000 hic.

B. The results are inconclusive regarding whether one of the booster seats could have a measurement that is greater than 1000 hic.

C. The requirement is met since most sample measurements are less than 1000 hic.

D. There is not strong evidence that the mean is less than 1000 hic, and one of the booster seats has a measurement that is greater than 1000 hic.

(1) a) Fail to reject                                    (2) a) insufficient

      b) Reject                                                     b) sufficient

9. The accompanying data table lists the weights of male college students in kilograms. Test the claim that male college students have a mean weight that is less than the 83 kg mean weight of males in the general population. Use a 0.01 significance level. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, and conclusion for the test.

Assume this is a simple random sample.

⁴Click the icon to view the sample data.

What are the null and alternative hypotheses?

A. H₀: m = 83 kg

     H₁: m > 83 kg

B. H₀: m = 83 kg

     H₁: m < 83 kg

C. H₀: m ¹ 83 kg

    H₁: m = 83 kg

D. H₀: m ¹ 83 kg

   H₁: m < 83 kg

Calculate the test statistic.

t= _______________________ (Round to three decimal places as needed. )

Identify the P-value.

The P-value is ________________________ . (Round to four decimal places as needed. )

State the final conclusion that addresses the original claim.

(1) _____________ H₀. There is (2) _____ evidence to conclude that male college students have a mean weight that is less than the 83 kg mean weight of males in the general population.

4: Weights of male college students

Full data set

Person	Weight	Person	Weight
1	73	17	80
2	97	18	65
3	74	19	54
4	90	20	73
5	59	21	77
6	71	22	74
7	67	23	74
8	92	24	65
9	67	25	64
10	68	26	64
11	87	27	66
12	81	28	71
13	60	29	65
14	70	30	75
15	68	31	74
16	68	32	94

 

(1) a) Fail to reject                 b) Reject

(2) a) Not sufficient               b) Sufficient

10. Which of the following is not a requirement for testing a claim about a population with o not known?

Choose the correct answer below.

A. The sample is a simple random sample.

B. Either the population is normally distributed or n > 30 or both.

C. The value of the population standard deviation is not known.

D. The population mean, m, is equal to 1.

11. Which of the following is not a characteristic of the t test?

Choose the correct answer below.

A. The Student t distribution is different for different sample sizes.

B. The t test is robust against a departure from normality.

C. The Student t distribution has the same general bell shape as the standard normal distribution.

D. The Student t distribution has a mean of t= 0 and a standard deviation of s = 1.

12. Which of the following is not a strategy for finding P-values with the Student t distribution?

Choose the correct answer below.

A. Use software such as Minitab, Excel, or STATDISK to find the P-value rounded to at least 4 decimal places.

B. Use the table in the book to find the P-value rounded to at least 4 decimal places.

C. Use a TI-83/84 Plus calculator to find the P-value rounded to at least 4 decimal places.

D. Use the table in the book with the appropriate number of degrees of freedom to find a range of values containing the P-value.

13. Which of the following is not true when using the confidence interval method for testing a claim about m when s is unknown?

Choose the correct answer below.

A. The P-value method, the traditional method, and the confidence interval method are equivalent and yield the same results.

B. Fora two-tailed hypothesis test with a 0.05 significance level, one must construct a 95% confidence interval.

C. The P-value method and the classical method are not equivalent to the confidence interval method in that they may yield different results.

D. Fora one-tailed hypothesis test with a 0.05 significance level, one must construct a 90% confidence interval.

14. Which of the following is NOT a requirement for testing a claim about a population mean with s known?

Choose the correct answer below.

A. Either the population is normally distributed or n > 30 or both.

B. The sample is a simple random sample.

C. The sample mean, x is greater than 30.

D. The value of the population standard deviation is known.

15. Which of the following is NOT a requirement for testing a claim about a mean with s known?

Choose the correct answer below.

A. If the sample results (or more extreme results) can easily occur when the null hypothesis is true, we attribute the relatively small discrepancy between the assumption and the sample results to chance.

B. If, under a given assumption, there is an exceptionally small probability of getting sample results at least as extreme as the results that were obtained, we conclude that the assumption is probably not correct.

C. A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.

D. If the sample results (or more extreme results) cannot easily occur when the null hypothesis is true, we explain the discrepancy between the assumption and the sample results by concluding that the assumption is true, so we do not reject the assumption.