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Question 1 You want to obtain a sample to estimate a population mean

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Question 1

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately ? = 21.9. You would like to be 95% confident that your esimate is within 0.2 of the true population mean. How large of a sample size is required?

n=

Do not round mid-calculation. However, use a critical z value accurate to two (2) decimal places.

Question 2 

A hypothesis test was conducted to investigate whether the population mean age of college students at Osler city is higher than 22.

1. This is a

0 two-tailed test.

0 left-tailed test.            

0 right-tailed test.

0 half-way test.

2. Select a correct formulation of the appropriate hypotheses:

H0: µ>22              H0: µ>_22            H0: µ<_22           

H1: µ<_22            H1: µ<22              H1: µ>22

 

H0: µ=22              H0: µ<22              H0: µ≠22

H1: µ≠22              H1: µ>_22            H1: µ=22

 

 

Question 3

You are conducting a study to test a claim that the mean income of regular casino visitors is significantly less than $75,000. A random sample of 85 regular casino visitors had a mean income of $64,782. Do the sample data provide convincing evidence to support the claim? Assume o is known to be $38,000. Conduct a hypothesis test using a 5% level of significance. Give numeric answers to at least 2 decimal places.

What are the correct hypotheses? (Select the correct symbols and values.)

Ho:  Select an answer

H1: Select ananswer

Based on the hypotheses, find the following:

Test Statistic =

Critical-value =

The correct decision is to :  Select an answer

The correct conclusion would be: Select an answer

 

that the mean income of regular casino visitors is significantly less than $75,000

 

 

 Question 4 •

Giving a test to a group of students, the grades and gender are summarized below

	A	B	C	Total
Male	2	12	20	34
Female	9	13	5	27
Total	11	25	25	61

 

If one student is chosen at random, Find the probability that the student %vas NOT a [female that got a "B"]

 

Question 5

Suppose (10,48) is a 90% confidence interval estimate for a population mean a µ)

The point estimate x is

b) The margin of error is

c) Which of the following are true statements?

I. There is a 0.90 probability thatµ is between 10 and 48.

II. There's a 90% chance that any particular value in the population will fall between 10 and 48.

III. 90% of confidence intervals constructed in this population will have a lower limit of 10 and an upper limit of 48.

IV. If 90% confidence intervals are calculated from all possible samples of the given size,µ is expected to be in 90% of these intervals.

0 1 and II

0 1 and III

0 11 and III

0 III only

0 I and IV

0 IV only

 

 Question 6

The annual rainfall in a certain region is approximately normally distributed with mean 41.7 inches and standard deviation 5.6 inches. Round answers to the nearest tenth of a percent.

a) What percentage of years will have an annual rainfall of less than 43 inches?

b) What percentage of years will have an annual rainfall of more than 38 inches?

c) What percentage of years will have an annual rainfall of between 37 inches and 42 inches?

Question 7

The number of people who survived the Titanic based on class and gender is in the following table. Suppose a person is picked at random from the survivors.

Class	Female	Male	Total
1st	135	60	195
2nd	93	26	119
3rd	81	57	138
Total	309	143	452

 

a) What is the probability that a survivor was male?

Round final answer to 3 decimal places.

b)What is the probability that a survivor was in the 1st class?

Round final answer to 3 decimal places.

c) What is the probability that a survivor was a male given that the person was in 1st class? Round final answer to 3 decimal places.

d) What is the probability that a survivor was a male and in the 1st class?

Round final answer to 3 decimal places.

e) What is the probability that a survivor was a male or in the 1st class?

Round final answer to 3 decimal places.

f) Are the events "survivor is a male" and "survivor is in 1st class" mutually exclusive? Why or why not?

Select an answer

g) Are the events "survivor is a mate" and "survivor is in 1st class" independent? Why or why not?

Select an answer

 

 Question 8

 According to a study, 80 % of adult smokers started smoking before 21 years old. 14 smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded.

1. The probability that at least 12 of them started smoking before 21 years of age is

2. The probability that at most 11 of them started smoking before 21 years of age is

3. The probability that exactly 4 of them started smoking before 21 years of age is

 

Question 9  

2.6 Dice Rolls: If you roll a pair of fair dice, what is the probability of each of the following? (round all answers to 4 decimal places)

a) getting a sum of 1? 

b) getting a sum of 5?

c) getting a sum of 12?  

 

Question 10

 In conducting the hypothesis test below, your sample consists of 16 observations, with a mean of 30 and standard deviation of 3.33.

Ho: µ >_ 30.1

H1 :µ < 30.1

a) This is a I Select an answer

b) Calculate the test statistic, rounded to 3 decimal places. T =

c) At a   = 0.05, the rejection region is

 O t < -2.131 or t >2.131   0 t > -1.753

0. t > -1.753                         none of the above

3. The decision is to

0 fail to reject Ho since the test statistic does not fall in the rejection region.

0 reject Ho since the test statistic falls in the rejection region.  

O fail to reject H, since the test statistic does not fall in the rejection region.

O reject H, since the test statistic falls in the rejection region.

O none of the above

 

 

• Question 11

Match each of the following statements with the terms and values below:

I - a

The sampling distribution of the sample mean becomes approximately normal as n becomes large

(Upper confidence limit - Lower confidence limit)/ 2

 A range of values of a sample statistic that likely contains the population parameter

we reject Ho at a = 0.05 we must also reject it at

Rejecting Ho: µ <_ 23 when in fact µ = 25

lf we fail to reject H0 at a= 0.03 we must also fail to reject it at

The decision when the test statistic falls outside the critical region

A single statistic that is used to estimate a population parameter

Failure to reject a false null hypothesis

1. Confidence interval
2. Type II error
3. Fail to reject Ho
4. Correct decision
5. a = 0.015
6. a = 0.08
7. Central Limit Theorem
8. Margin of Error
1. Point estimate
10. Confidence level

Question 12

If n = 25, -± = 50, and 8 = 3, construct a confidence interval at a 95 % confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place.

<µ<                       

 

Question 13

A population of values has a normal distribution with µ = 47 and ó = 3.9. You intend to draw a random sample of size n = 13.

Round z to two (2) decimal places and final answer to 4 decimal places.

Find the probability that a single randomly selected value is greater than 49.3.

P(x > 49.3) =

Find the probability that a sample of size n=13 is randomly selected with a mean greater than 49.3.

P(x > 49.3) =

 

Question 14

Testing:

Ho: µ ≤  19.1

H1: µ > 19.1

Your sample consists of 20 values, with a sample mean of 20.3. Suppose the population standard deviation is known to be 2.87.

a) Calculate the value of the test statistic, rounded to 2 decimal places.

z 

 

b) At a = 0.03, the rejection region is

 O z>2.17

 0 z < -1.88 or z> 1.88

O z <-2.17

0 z < -2.17 or z > 2.17

0 z < -1.88

Oz > 1.88

c) The decision is to

Reject the null hypothesis .

Accept the alternative hypothesis

Fail to reject the null hypothesis

Accept the null hypothesis

4. Supposed you mistakenly failed to reject the null hypothesis in this problem, what type of error is that? Type II Type I