QUESTION 1 Provide an appropriate response. True or False: The general form of a

Question

QUESTION 1

Provide an appropriate response.

True or False: The general form of a large-sample (1 - ) 100% confidence interval for a population proportion p is where = is the sample proportion of observations with the characteristic of interest.

False
True

4 points   

QUESTION 2

Find the t-value.

Find the critical t-value that corresponds to 95% confidence and n = 16.

1.753
2.131
2.602
2.947

4 points   

QUESTION 3

Provide an appropriate response.

True or False: The chi-square distribution is a symmetric distribution for all degrees of freedom.

False
True

4 points   

QUESTION 4

Provide an appropriate response.

A researcher wishes to estimate the number of households with two computers. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 3%? A previous study indicates that the proportion of households with two computers is 20%.

966
1474
5
1179

4 points   

QUESTION 5

Provide an appropriate response.

A confidence interval for p can be constructed using

p ± z/2
± z
p ± z
± z/2

4 points   

QUESTION 6

Provide an appropriate response.

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use a 98% confidence interval to estimate the true proportion of students on financial aid. Express the answer in the form ± E and round to the nearest thousandth.

0.59 ± 0.564
0.59 ± 0.003
0.59 ± 0.081
0.59 ± 0.006

4 points   

QUESTION 7

Provide an appropriate response.

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 4% with 90% reliability, how many students would need to be sampled?

249
410
99
17

4 points   

QUESTION 8

Provide an appropriate response.

To select the correct Student's t-distribution requires knowing the degrees of freedom. How many degrees of freedom are there for a sample of size n?

n
n - 1
n + 1

4 points   

QUESTION 9

Provide an appropriate response.

The mean number of rushing yards for one NFL team was less than 105 yards per game. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

There is sufficient evidence to support the claim < 105.
There is not sufficient evidence to reject the claim < 105.
There is not sufficient evidence to support the claim < 105.
There is sufficient evidence to reject the claim < 105.

4 points   

QUESTION 10

Provide an appropriate response.

Find the standardized test statistic t for a sample with n = 12, = 19.5, s = 2.1, and if Round your answer to three decimal places.

-0.825
-0.037
-0.381
-0.008

4 points   

QUESTION 11

Provide an appropriate response.

A survey claims that 9 out of 10 doctors (i.e., 90%) recommend brand Z for their patients who have children. To test this claim against the alternative that the actual proportion of doctors who recommend brand Z is less than 90%, a random sample of 100 doctors results in 83 who indicate that they recommend brand Z. The test statistic in this problem is approximately (round to the nearest hundredth):

-2.33
2.33
-1.99
-1.83

4 points   

QUESTION 12

Provide an appropriate response.

Find the critical value for a right-tailed test with = 0.05.

1.28
1.96
1.645
2.33

4 points   

QUESTION 13

Provide an appropriate response.

Suppose you want to test the claim that = 3.5. Given a sample size of n = 51 and a level of significance of when should you reject H0 ?

Reject H0 if the standardized test statistic is greater than 1.96 or less than -1.96
Reject H0 if the standardized test statistic is greater than 1.645 or less than -1.645
Reject H0 if the standardized test statistic is greater than 2.575 or less than -2.575.
Reject H0 if the standardized test statistic is greater than 2.33 or less than -2.33.

4 points   

QUESTION 14

Provide an appropriate response.

The power of the test is

.
.
1 - .
1 - .

4 points   

QUESTION 15

Provide an appropriate response.

The mean monthly gasoline bill for one household is greater than $120. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

There is not sufficient evidence to support the claim > $120.
There is sufficient evidence to support the claim > $120.
There is not sufficient evidence to reject the claim > $120.
There is sufficient evidence to reject the claim > $120.

4 points   

QUESTION 16

Provide an appropriate response.

A local tennis pro-shop strings tennis rackets at the tension (pounds per square inch) requested by the customer. Recently a customer made a claim that the pro-shop consistently strings rackets at lower tensions, on average, than requested. To support this claim, the customer asked the pro shop to string 6 new rackets at 42 psi. Suppose the two-tailed P-value for the test described above (obtained from a computer printout) is Give the proper conclusion for the test. Use

There is insufficient evidence to conclude that , the true mean tension of the rackets, is less than 42 psi.
There is sufficient evidence to conclude that , the true mean tension of the rackets, is less than 42 psi.
Accept H0 and conclude that , the true mean tension of the rackets, equals 42 psi.
Reject H0 and conclude that , the true mean tension of the rackets, equals 42 psi.

4 points   

QUESTION 17

Provide an appropriate response.

The probability of making a Type II error is indicated by the letter

4 points   

QUESTION 18

Provide an appropriate response.

A random sample of 160 car purchases are selected and categorized by age. The results are listed below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the group, 31% for the 45-65 group, and 12% for the group over 65. Find the critical value to test the claim that all ages have purchase rates proportional to their driving rates.

11.143
9.348
7.815
6.251

4 points   

QUESTION 19

Provide an appropriate response.

A random sample of 160 car purchases are selected and categorized by age. The results are listed below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the group, 31% for the 45-65 group, and 12% for the group over 65. Find the P-value to test the claim that all ages have purchase rates proportional to their driving rates.

0.01 < P-value < 0.025
P-value > 0.10
0.005 < P-value < 0.01
P-value < 0.005

4 points   

QUESTION 20

Provide an appropriate response.

A teacher figures that final grades in the chemistry department are distributed as: A, 25%; F, 5%. At the end of a randomly selected semester, the following number of grades were recorded. Find the critical value to determine if the grade distribution for the department is different than expected. Use = 0.01.

7.779
15.086
9.488
13.277

4 points   

QUESTION 21

Provide an appropriate response.

A teacher figures that final grades in the chemistry department are distributed as: A, 25%; F, 5%. At the end of a randomly selected semester, the following number of grades were recorded. Find the P-value to determine if the grade distribution for the department is different than expected. Use = 0.01.

P-value < 0.005
0.025 < P-value < 0.05
P-value > 0.10
0.01 < P-value < 0.025

4 points   

QUESTION 22

Provide an appropriate response.

A spinner is mounted on a piece of cardboard divided into six areas of equal size. Each of the six areas is a different color (blue, yellow, red, green, white and orange). When the spinner is spun, each color should be selected by the spinner approximately of the time. A student suspects that a certain spinner is defective. The suspected spinner is spun 90 times. The results are shown below. Find the critical value to test the student's claim. Use = 0.10.

1.610
10.645
9.236
11.071

4 points   

QUESTION 23

Provide an appropriate response.

A teacher figures that final grades in the chemistry department are distributed as: A, 25%; F, 5%. At the end of a randomly selected semester, the following number of grades were recorded. Calculate the chi-square test statistic to determine if the grade distribution for the department is different than expected. Use = 0.01.

5.25
0.6375
6.87
4.82

4 points   

QUESTION 24

Provide an appropriate response.

A sports statistician is interested in determining if there is a relationship between the number of home team and visiting team losses and different sports. A random sample of 526 games is selected and the results are given below. Find the critical value to test the claim that the number of home team and visiting team losses is independent of the sport. Use = 0.01.

9.348
7.815
12.838
11.345

4 points   

QUESTION 25

Provide an appropriate response.

A __________________ test is an inferential procedure used to determine whether a frequency distribution follows a defined distribution.

goodness-of-fit
normality
F
2

Explanation / Answer

Find the critical t-value that corresponds to 95% confidence and n = 16.

n-1=16-1=15

alpha=0.05

alpha/2=0.05/2=0.025

t xrit for 15 df and 0.025 level of signiifcance

=2.131

2.131

To select the correct Student's t-distribution requires knowing the degrees of freedom. How many degrees of freedom are there for a sample of size n?

ANS

n-1

QUESTION 5

Provide an appropriate response.

A confidence interval for p can be constructed using

p ± z/2

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