6.3: Hypothesis Testing with t-Scores

What is the magnitude (ignore mathematical sign) of the critical value for a two-tailed hypothesis test, with:

α=0.01

n=20

s=1.35

a) Critical value = 2.539.

b) Critical value = 2.845.

c) Critical value = 2.861.

d) Critical value = 2.580.

c) Critical value = 2.861.

What is the proper conclusion to a hypothesis test using the information below:

a) Do not reject the alternative hypothesis because the test statistic is in the acceptance region.

b) Do not reject the null hypothesis because the test statistic is in the acceptance region.

c) Do reject the null hypothesis because the test statistic is in the rejection region.

d) Do reject the null hypothesis because the test statistic is less than zero (0).

b) Do not reject the null hypothesis because the test statistic is in the acceptance region.

What is the proper conclusion to a hypothesis test using the information below:

a) Do reject the null hypothesis because p-value is larger than alpha.

b) Do not reject the null hypothesis because p-value is larger than alpha.

c) Not enough information is given to make a conclusion.

d) Do reject the null hypothesis because p-value does not equal alpha.

b) Do not reject the null hypothesis because p-value is larger than alpha.

What is the p-value for a two-tail hypothesis test using the information below:

μ=15

α=0.10

n=51

xbar=16.25

s=3.0

a) p-Value = 0.003.

b) p-Value = 0.005.

c) p-Value = 0.0025.

d) p-Value = 0.010.

b) p-Value = 0.005.

What is the magnitude (ignore mathematical sign) of the critical value for a left-tailed hypothesis test, with:

α=0.10

n=13

s=11.93

a) Critical value = 1.64.

b) Critical value = 1.782.

c) Critical value = 1.350.

d) Critical value = 1.356.

d) Critical value = 1.356.

What is the magnitude (ignore mathematical sign) of the critical value for a right-tailed hypothesis test, with:

α=0.05

n=15

s=4.00

a) Critical value = 1.761.

b) Critical value = 2.145.

c) Critical value = 2.131

d) Critical value = 1.96.

a

What is the proper conclusion to a hypothesis test using the information below:

a) Do not reject the null hypothesis because the test statistic is in the acceptance region.

b) Do not reject the alternative hypothesis because the test statistic is in the rejection region.

c) Do reject the null hypothesis because the test statistic is in the rejection region.

d) Do reject the null hypothesis because the test statistic is less than zero (0).

c) Do reject the null hypothesis because the test statistic is in the rejection region.

What is the proper conclusion to a hypothesis test using the information below:

a) Do reject the null hypothesis because p-value is less than alpha.

b) Do not reject the null hypothesis because p-value is less than alpha.

c) A critical value and a test statistic is needed to make a conclusion in a hypothesis test.

d) Do reject the null hypothesis because p-value does not equal alpha.

a

What is the value of the test statistic for a two-tail hypothesis test using the information below:

μ=8.0

α=0.02

n=15

x bar=7.3

s=1.8

a) t0=−2.73

b) t=+1.10

c) t0=−1.51

d) t0=−5.83

c) t0=−1.51

What is the value of the test statistic for a right-tail hypothesis test using the information below:

μ=8.0

α=0.05

n=25

xbar=8.9

s=1.8

a) t0=+2.73

b) t0=−5.83

c) t0=+1.10

d) t0=+2.5

d) t0=+2.5

What is the p-value for a right-tail hypothesis test using the information below:

μ=65

α=0.05

n=23

xbar=70.6

s=12.3

a) p-Value = 0.02 .

b) p-Value = 0.04 .

c) p-Value = 0.01 .

d) p-Value = 1.02 .

a

Use the information below to perform the appropriate hypothesis test at a 0.05 level of significance.

There is prior evidence that lawn mower engines will run for a mean of 300 minutes on a gallon of gasoline. An amateur inventor develops a new lawn mower engine that he claims will run for more than 300 minutes on a gallon of gasoline. To find out, a local consumer agency took 51 of the new engines and ran them each on a gallon of gasoline. They found a average run time of 305 minutes with a standard deviation of 30 minutes. Is the amateur inventor's claim correct? Please find out.

a) Yes, the amateur inventor's claim is correct, because the p-value is greater than alpha (α).

b) Yes, the amateur inventor's claim is correct, because the test statistic is in the acceptance region of the schematic curve.

c) No, the amateur inventor's claim is not correct, because the test statistic is less than zero (0).

d) No, the amateur inventor's claim is not correct, because the test statistic = 1

d) No, the amateur inventor's claim is not correct, because the test statistic = 1.19 and the critical value = 1.676.

Use the information below to match the following statistics with their appropriate value .

There is prior evidence that lawn mower engines will run for a mean of 240 minutes on a gallon of gasoline. An amateur inventor develops a new lawn mower engine that he claims will run for more than 240 minutes on a gallon of gasoline. To find out, a local consumer agency took 36 of the new engines and ran them each on a gallon of gasoline. They found a average run time of 249 minutes with a standard deviation of 41 minutes. Is the amateur inventor's claim correct? Please perform a hypothesis test at a 0.05 level of significance to find out.

A. The p-value

B. The conclusion

C. The value of the test statistic

-+1.32

-0.10

-Do not reject H(0) - the inventor's claim is not correct.

c, a , b

Use the information below to match the following statistics with their appropriate value .

A measure of how hard is a material is the Brinell scale. An engineer does not believe that the hardness of a new metal alloy he invented is equal to a Brinell score of 170. To find out, he took 25 pieces of the new alloy and measured their hardness, finding an average score of 174.52 and a standard deviation score of 10.31. Please perform a hypothesis test at a 0.01 level of significance to find out.

A. The conclusion

B. The value of the test statistic

C. The p-value

-+2.19

-0.04

-Do not reject H(0) - the engineer's claim is not correct.

b, c, a

Use the information below to match the following statistics with their appropriate value .

A nutritionist believes that teenagers who don't eat fast food intake fewer calories each day. Earlier, the nutritionist had studied teenagers who do eat fast food and found they consumed a mean of 2,637 calories per day. To answer her question, the nutritionist then studied teenagers who do not eat fast food. She measured 61 teens for their calorie intake and found an average of 2,258 calories with a standard deviation of 1,519 calories. Please perform a hypothesis test at a 0.10 level of significance to find out.

A. The value of the test statistic

B. The conclusion

C. The p-value

--1.95

-0.025

-Do reject H(0) - the nutritionist's claim is correct.

a, c, b

Use the information below to match the following statistics with their appropriate value.

A local company making batteries for electric bicycles claim that their batteries have a mean lifetime of 2.1 years under normal use. A local store renting electric bicycles decided to find out if these batteries had a different lifetime. The store randomly chose 10 bicycles and measured the time it took for the batteries to fail, finding an average lifetime of 2.14 years with a standard deviation of 0.18 years. Please perform a hypothesis test at a 0.05 level of significance to find out.

A. The p-value

B. The conclusion

C. The value of the test statistic

-+0.70c

-0.500a

-Do not reject H(0) - the store's claim is not correct.b

c, a, b

Use the information below to match the following statistics with their appropriate value .

Your boss in the human resources department at a local company asks you to find out if the employee's monthly allowances need to be raised because of inflation. Employee monthly allowances are now set at $500 per month. To answer this question with evidence, you randomly select 40 employees and measure how much they spend each month, finding an average of $640 and a standard deviation of $250. Please perform a hypothesis test at a 0.05 level of significance to find out.

A. employee's allowances have gone up.

B. The value of the test statistic

C. The p-value

-+3.54

-0.0005

-Do reject H(0) - employee's allowances have gone up.

b, c, a

Use the information below to match the following statistics with their appropriate value.

An owner of a small company in interested in a new computer training program for employees, but she wants to make sure that it is effective in her company before purchasing it. She directs you to find out, so you randomly select 10 employees and measure their improvement in score by giving them a test both before and after the program. Then the difference is calculated and recorded, finding an average difference of 2.6 with a standard deviation difference of 2.93. Please perform a hypothesis test at a 0.10 level of significance to find out.

A. The p-value

B. The conclusion

C. The value of the test statistic

-+2.81

-0.01

-Do reject H(0) - there is an improvement in scores.

c, a, b

Use the information below to match the following statistics with their appropriate value .

An instructor teaches a large statistics course at a local university and wonders how this semester's students are doing. She knows that in prior semesters students had a mean score of 75 on the final exam, and she doesn't think that this semester's students will score the same. To find out, she randomly selects 31 students and measures this semester's final exam score. She finds an average score of 77 and a standard deviation score of 16.54. Please perform a hypothesis test at a 0.01 level of significance to find out.

A. Do not reject H(0) - students did score the same as before.

B. The value of the test statistic

C. The p-value

-+0.67

-0.50

-Do not reject H(0) - students did score the same as before.

b, c, a