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University of Pittsburgh - STAT 0200 CH 3 1)Using the 68-95-99

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University of Pittsburgh - STAT 0200

CH 3

1)Using the 68-95-99.7 rule, what percentage of students score below 62?

 

 

 

2. Using the standard Normal distribution tables, the area under the standard Normal curve corresponding to Z > –1.62 is what? Sketch the standardized curve and find the area.

 

Use Table A to get the area for Z < -1.62.

 

Use the following to answer Questions 3 and 4

 

Birth weights at a local hospital have a Normal distribution with a mean of 110 oz and a standard deviation of 15 oz. 

 

3. The proportion of infants with birth weights above 125 oz is

µ = 110 oz; sigma = 15 oz.; x = 125 oz.

 

 

4. The proportion of infants with birth weights between 125 oz and 140 oz is

µ = 110 oz; sigma = 15 oz.; x₁ = 125 oz.; x₂ = 140.

 

 

CH 11

 

1. The incomes in a certain large population of college teachers have a normal distribution with mean $75,000 and standard deviation $10,000. Four teachers are selected at random from this population to serve on a committee. What is the probability that their average salary is less than $65,000?

 

μ = 75,000

σ = 10,000

n = 4

x bar = 65,000

 

 

2. The central limit theorem says that when a simple sample of size n is drawn from any population with mean μ and standard deviation σ, then when n is sufficiently large

 

 

Use the following for questions 3-5.

 

A manufacturing process produces bags of cookies. The distribution of content weights of these bags is Normal with mean 15.0 oz and standard deviation 1.0 oz. We will randomly select n bags of cookies and weigh the contents of each bag selected.

 

3. Which of the following statements is true with respect to the sampling distribution of the sample mean, x bar ?

 

a. If the sample size, n, increases, the standard deviation of x will decrease.

b. If the population standard deviation increases, the standard deviation of x will increase.

c. According to the law of large numbers, if the sample size, n, increases, x will tend to be closer to 15 ounces.

 d. All of the above.

 

4. How many bags should be selected so that the standard deviation of the sample mean is 0.1 ounces?

σ = 1.0

n = ?

 

 

 

 

 

 

 

5. If 100 bags of cookies are selected randomly, the probability that the sample mean will be between 14.9 and 15.1 ounces is

μ = 15.0

σ = 1.0

n = 100

x bar₁ = 14.9

x bar₂ = 15.1

 

 

 

 

CH 14

 

1. A researcher selects a random sample. A 90% confidence interval for a population mean μ

 

a. is an interval with margin of error ± 90%.

 b. has the property that if we repeatedly selected our random sample in exactly the same way, each time constructing a different 90% confidence interval for μ, then in the long run 90% of those intervals would contain μ.

c. (a) and (b) are both true.

d. is an interval that has width .90.

 

Use the following to answer questions 2-3.

 

A researcher used a new drug to treat 100 subjects with high cholesterol. For the patients in the study, after two months of treatment the average decrease in cholesterol level was 80 milligrams per deciliter (mg/dl). Assume that the decrease in cholesterol after two months of taking the drug follows a Normal distribution, with unknown mean μ and standard deviation σ = 20 mg/dl. The researcher will construct a 90% confidence interval to estimate μ.

 

2. The margin of error associated with a 90% confidence interval for the researcher’s 90% confidence interval for μ is

 

σ = 20 mg/dl

n = 100

C = 90 %

m = ?

 

 

3. The researcher’s 90% confidence interval for μ is

x bar = 80 mg

 

 

 

CH 15

 

1. Is the mean age at which American children can first read now under 4 years? If the population of all American children has mean age of μ years until they begin to read and standard deviation σ years, what are the null and alternative hypotheses to research this?

 

 

Use the following to answer questions 2-3.

 

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution, with mean of 115 and standard deviation 25. A researcher suspects that incoming freshmen have a mean μ, which is different from 115, because they are often excited yet anxious about entering college. To verify her suspicion, she tests the hypotheses

H₀: μ = 115

Ha: μ ≠ 115.

The researcher gives the SSHA to 100 incoming freshmen and observes a mean score of 119. Assume that the scores of all incoming freshmen are approximately Normal with the same standard deviation as the scores of all college students.

 

2. The P-value for this test is

 

μ = 115

σ = 25

n = 100

x bar = 119

two-sided

 

 

3. Based on the P-value computed in problem 21 above,

 a. the data are not statistically significant at α = .05 and not statistically significant at α = .01. [P-value is greater than each value of alpha; therefore, we cannot reject H₀ at either significance level]

b. the data are statistically significant at α = .05 and at α = .01.

c. the data are statistically significant at α = .05, but not at α = .01.

d. the data are statistically significant at α = .01, but not at α = .05.

 

4. If the researcher deems the data to be statistically significant, which of the following is true with respect to a conclusion reached?

 

 a. The researcher has strong enough evidence to conclude that the average freshmen SSHA score differs from that of the average SSHA score for all college students.

b. The researcher does not have strong enough evidence to conclude that the average freshmen SSHA score differs from that of the average SSHA score for all college students.

c. The researcher has proven that the mean SSHA score for freshmen is, in fact, 115.

d. The researcher has proven that the mean SSHA score for freshmen is not 115.