ANSWERS 20 MATH MCQ's

Question 1

The heights (in feet) of a sample of five randomly chosen students from School x are 6.3, 6.1, 5.7, 5.8, and 6.2.  Determine a 90% confidence interval for the mean height of all students at School x. 

Note: In the answers below, "sqrt" denotes the square root.

a. 6.02 ± 1.645*[.259/sqrt(5)] 

b. 6.02 ± 2.015*[.259/sqrt(5)] 

c. 6.02 ± 2.132*[.259/sqrt(5)] 

d. 6.02 ± 1.28*[.259/sqrt(5)] 

e. 6.02 ± 2.132*[.259/sqrt(4)]

Question 2 .     

Refer to question 1.  What is a?

a. 0

b. .05

c. .1

d. .5

e. .9

Question 3 .     

To determine how many hours per week freshmen college students watch television, a random sample of 225 students was selected.  It was determined that the students in the sample spent an average of 35 hours watching TV per week.  The population standard deviation is known to be 12 hours.  Provide a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week.

a. 35 ± 1.645*[12/sqrt(225)] 

b. 35 ± 1.96*[12/sqrt(225)] 

c. 35 ± 1.645*[3.46/sqrt(225)] 

d.35 ± 1.96*[12/sqrt(224)]

Question 4 .     

Refer to question 3.  Compute the population standard deviation.

a. 35

b. 12

c. .8

d. .053

Question 5 .     

A supermarket wants to test whether the mean weight of the cans of peas sold by a particular maker equals 24 oz.  It chooses a random sample of 16 cans and finds that the sample mean is 23.3 oz and the sample standard deviation is .4 oz.  Your job is to test, at the 5% level of significance, whether or not the mean weight equals 24 oz.

What are the null and alternative hypotheses?

a. Ho: μ = 24, Ha: μ ≠ 24 

b. Ho: μ ≤ 24, Ha: μ > 24 

c. Ho: μ ≥ 24, Ha: μ 40 

d. Ho: μ ≥ 40, Ha: μ < 40 

e. Ho: μ = 43, Ha: μ ≠ 43

Question 6 .     

Refer to question 5.  What is a?

a. .95

b. .025

c. .05

d. .10

Question 7 .     

Refer to question 5.  What is (are) your critical value(s)?  Remember, the critical value(s) define your rejection region.

a. 1.96 

b. ± 1.96 

c. ± 1.645 

d. ± 2.120

e. ± 2.131

Question 8 .     

Refer to question 5.  What is the value of your test statistic?

a. 7.00

b. -7.00 

c. -1.75

d. 0

e. None of these responses

Question 9 .     

Refer to question 5.  What is your conclusion?

a. Reject the null hypothesis at the 5% level 

b. Fail to reject the null hypothesis at the 5% level 

c. Reject the null hypothesis at the 2.5% level

d. Fail to reject the null hypothesis at the 2.5% level 

e. None of these responses

Question 10 .     

In order to determine the average price of hotel rooms in Small Town, U.S.A., a sample of 64 hotels was selected.  It was determined that the average price of the rooms in the sample was $43.   The population standard deviation is known to be $10.  Your job is to use a 5% level of significance and determine whether or not the average room price is significantly different from $40 using the p-value approach.

What are your null and alternative hypotheses? 

a. Ho: μ = 40, Ha: μ ≠ 40 

b. Ho: μ ≤ 40, Ha: μ > 40 

c. Ho: μ ≥ 40, Ha: μ < 40 

d. Ho: μ = 43, Ha: μ ≠ 43

Question 11 .     

Refer to question 10.  Compute the test statistic. 

a. 43

b. -2.4

c. 2.4

d. .3

Question 12 .     

Refer to question 10.  Compute the p-value. 

a. .05 

b. .025 

c. .0082 

d. .4918 

e. Need a computer to determine the p-value here

Question 13 .     

Refer to question 10.  The rejection region(s) is (are)

a. Located in the upper 5% of the sampling distribution of x-bar.

b. Located in the lower 5% of the sampling distribution of x-bar.

c. Split evenly on each side of the sampling distribution of x-bar so that there is one rejection region in the lower 2.5% of the sampling distribution of x-bar and another in the upper 2.5% of the sampling distribution of x-bar.

d. Split evenly on each side of the sampling distribution of x-bar so that there is one rejection region in the lower 5% of the sampling distribution of x-bar and another in the upper 5% of the sampling distribution of x-bar.

Question 14 .     

Refer to question 10.  What is a?

a. .025

b. .05

c. .075

d. .95

Question 15 .     

Refer to question 10.  What is your conclusion?

a. Reject the null hypothesis at the 5% level 

b. Fail to reject the null hypothesis at the 5% level 

c. Reject the null hypothesis at the 2.5% level 

d. Fail to reject the null hypothesis at the 2.5% level 

e. Reject the null hypothesis at the 95% level

Question 16 .     

The two-tailed p-value (“p”) is defined as the upper tail probability associated with a positive test statistic or the lower tail probability associated with a negative test statistic.  When using the p-value approach to perform two-tailed tests, this p is sometimes doubled, and compared directly to α. 

a. True

b. False

c. This is not a possible response.

d. This is not a possible response.

  

Question 17 .     

When s is used to estimate s, the margin of error is computed by using the

a. normal distribution

b. Student's t distribution

c. the mean of the sample

d. the mean of the population

Question 18 .     

For the interval estimation of m when s is known and the sample is large, the proper distribution to use is

a. the normal distribution

b. the t distribution with n degrees of freedom

c. the t distribution with n + 1 degrees of freedom

d. the t distribution with n + 2 degrees of freedom

Question 19 .     

An assumption made about the value of a population parameter is called a

a. hypothesis

b. conclusion

c. confidence

d. significance

Question 20 .     

In order to determine an interval estimate for the mean of a population with unknown standard deviation a sample of 61 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is

a. 22

b. 23

c. 60

d. 61