QUESTIONS
Question 1
Using the information above, choose the correct conclusion that interprets the results within the context of the hypothesis test.
- We should reject the null hypothesis because t0<tα. So, at the 10%significance level, the data provide sufficient evidence to conclude that the average percentage of tips received by waitstaff in Chicago restaurants is less than 15%.
- We should not reject the null hypothesis because t0<tα. So, at the 10%significance level, the data do not provide sufficient evidence to conclude that the average percentage of tips received by waitstaff in Chicago restaurants is less than 15%.
- We should reject the null hypothesis because t0>tα. So, at the 10%significance level, the data provide sufficient evidence to conclude that the average percentage of tips received by waitstaff in Chicago restaurants is less than 15%.
- We should not reject the null hypothesis because t0>tα. So, at the 10%significance level, the data do not provide sufficient evidence to conclude that the average percentage of tips received by waitstaff in Chicago restaurants is less than 15%.
Question 2
Olivia gathered data on the average percentage of tips received by waitstaff in 31 restaurants in Chicago. She works through the testing procedure:
- H0:μ=15; Ha: μ<15
- α=0.10(significance level)
- The test statistic is t0 = (x¯−μ0) / s/√ = −1.16.
- The critical value is −t10=−1.310.
Conclude whether to reject or not reject H0. Select two responses below.
Reject H0.
Fail to reject H0.
The test statistic falls within the rejection region.
The test statistic is not in the rejection region.
Question 3
A linguistics expert is interested in learning about the amount of time people in his industry spend studying a new language. A random sample of 15 people in his industry were surveyed for a hypothesis test about the mean time people studied a new language last year. He conducts a one-mean hypothesis test, at the 10% significance level, to test the recent publication that the amount of time people in his industry are studying a new language was 30 minutes per week.
| df | t0.10 | t0.05 | t0.025 | t0.01 | t0.005 |
| …… | … | … | … | … | … |
| 1313 | 1.350 | 1.771 | 2.160 | 2.650 | 3.012 |
| 1414 | 1.345 | 1.761 | 2.145 | 2.624 | 2.997 |
| 1515 | 1.341 | 1.753 | 2.131 | 2.602 | 2.947 |
| 1616 | 1.337 | 1.746 | 2.120 | 2.583 | 2.921 |
Determine the critical value(s) using the partial t−table above. If entering two critical values, use ±.
Question 4
LaNai is a sergeant in the Marines who developed a new training program geared to reduce the time it takes to complete a particular obstacle course. After evaluating 14 random participants of the program, she conducted a hypothesis test about the mean time using a significance level of 1%. Preprogram evaluation revealed a mean of 20 minutes to complete the obstacle course.
| df | t0.10 | t0.05 | t0.025 | t0.01 | t0.005 |
| …… | … | … | … | … | … |
| 1313 | 1.350 | 1.771 | 2.160 | 2.650 | 3.012 |
| 1414 | 1.345 | 1.761 | 2.145 | 2.624 | 2.997 |
| 1515 | 1.341 | 1.753 | 2.131 | 2.602 | 2.947 |
| 1616 | 1.337 | 1.746 | 2.120 | 2.583 | 2.921 |
Determine the critical value(s) using the partial t−table above. If entering two critical values, use ±.
Question 5
Bruce, a store owner, would like to determine if a new advertising initiative has increased his sales per day compared to last year. He gathers information on 14 random sales days and conducts a hypothesis test about the sales revenue during a day using a significance level of 0.5 %. The mean revenue per day prior to the initiative was 650 dollars.
| df | t0.10 | t0.05 | t0.025 | t0.01 | t0.005 |
| …… | … | … | … | … | … |
| 1313 | 1.350 | 1.771 | 2.160 | 2.650 | 3.012 |
| 1414 | 1.345 | 1.761 | 2.145 | 2.624 | 2.997 |
| 1515 | 1.341 | 1.753 | 2.131 | 2.602 | 2.947 |
| 1616 | 1.337 | 1.746 | 2.120 | 2.583 | 2.921 |
Determine the critical value(s) using the partial t−table above. If entering two critical values, use ±.
Question 6
A new city Mayor would like to determine if community members are paying less for gas prices in his city this year compared to last year. He surveys 16 random community members and conducts hypothesis test about the mean cost of gas prices, which was 2.45 dollars last year, using a 5% significance level.
| df | t0.10 | t0.05 | t0.025 | t0.01 | t0.005 |
| …… | … | … | … | … | … |
| 1313 | 1.350 | 1.771 | 2.160 | 2.650 | 3.012 |
| 1414 | 1.345 | 1.761 | 2.145 | 2.624 | 2.997 |
| 1515 | 1.341 | 1.753 | 2.131 | 2.602 | 2.947 |
| 1616 | 1.337 | 1.746 | 2.120 | 2.583 | 2.921 |
Determine the critical value(s) using the partial t−table above. If entering two critical values, use ±.
Question 7
Dr. da Vinci would like to determine if a new drug to treat high blood pressure has had an effect on clients that he diagnosed with high blood pressure. He gathers the appropriate data on 16 random clients, and conducts a hypothesis test about the mean blood pressure after taking the medication using a significance level of 1 %. The mean blood pressure of these clients was 165/96 before taking the medication.
| df | t0.10 | t0.05 | t0.025 | t0.01 | t0.005 |
| …… | … | … | … | … | … |
| 1313 | 1.350 | 1.771 | 2.160 | 2.650 | 3.012 |
| 1414 | 1.345 | 1.761 | 2.145 | 2.624 | 2.997 |
| 1515 | 1.341 | 1.753 | 2.131 | 2.602 | 2.947 |
| 1616 | 1.337 | 1.746 | 2.120 | 2.583 | 2.921 |
Determine the critical value(s) using the partial t−table above. If entering two critical values, use ±.
Question 8
Vae, a nurse practioner, is interested in determining if her clients with type II diabetes have lower fasting glucose after they started a new nutritional plan. She measures the fasting glucose of 14 random clients, and conducts a hypothesis test about mean of fasting glucose using a significance level of 2.5 %. The mean fasting glucose in these clients was 165 before the nutritional plan.
| df | t0.10 | t0.05 | t0.025 | t0.01 | t0.005 |
| …… | … | … | … | … | … |
| 1313 | 1.350 | 1.771 | 2.160 | 2.650 | 3.012 |
| 1414 | 1.345 | 1.761 | 2.145 | 2.624 | 2.997 |
| 1515 | 1.341 | 1.753 | 2.131 | 2.602 | 2.947 |
| 1616 | 1.337 | 1.746 | 2.120 | 2.583 | 2.921 |
Determine the critical value(s) using the partial t−table above. If entering two critical values, use ±.
Question 9
Using the information above, choose the correct conclusion that interprets the results within the context of the hypothesis test.
- We should reject the null hypothesis because t0<tα. So, at the 1%significance level, the data provide sufficient evidence to conclude that the average amount spent on groceries is greater than $191.
- We should not reject the null hypothesis because t0<tα. So, at the 1%significance level, the data do not provide sufficient evidence to conclude that the average amount spent on groceries is greater than $191.
- We should reject the null hypothesis because t0>tα. So, at the 1%significance level, the data provide sufficient evidence to conclude that the average amount spent on groceries is greater than $191.
- We should not reject the null hypothesis because t0>tα. So, at the 1%significance level, the data do not provide sufficient evidence to conclude that the average amount spent on groceries is greater than $191.
Question 10
As a part of her studies, Terra gathered data on the amount spent weekly on groceries for a sample of 27 households. She works through the testing procedure:
- H0: μ=$191; Ha: μ>$191
- α=0.01(significance level)
- The test statistic is t0 = (x¯−μ0) / s/√n = 3.321.
- The critical value is t01 = 2.479.
Conclude whether to reject or not reject H0. Select two responses below.
- Reject H0.
- Fail to reject H0.
- The test statistic falls within the rejection region.
- The test statistic is notin the rejection region.
Question 11
As a part of her studies, Lexie gathered data on the speeds of 19 vehicles traveling on a highway. She works through the testing procedure:
- H0: μ=58; Ha: μ<58
- α=0.05
- The test statistic is t0 = (x¯−μ0) / s/√n = −0.943.
- The critical value is −t05 = −1.734.
At the 5% significance level, does the data provide sufficient evidence to conclude that the mean speed of vehicles traveling on the highway is less than 58 miles per hour?
- We should reject the null hypothesis because t0<tα. So, at the 5%significance level, the data provide sufficient evidence to conclude that the average speed of vehicles traveling on the highway is less than 58 miles per hour.
- We should not reject the null hypothesis because t0<tα. So, at the 5% significance level, the data do not provide sufficient evidence to conclude that the average speed of vehicles traveling on the highway is less than 58 miles per hour.
- We should reject the null hypothesis because t0>tα. So, at the 5%significance level, the data provide sufficient evidence to conclude that the average speed of vehicles traveling on the highway is less than 58 miles per hour.
- We should not reject the null hypothesis because t0>tα. So, at the 5% significance level, the data do not provide sufficient evidence to conclude that the average speed of vehicles traveling on the highway is less than 58 miles per hour.
ANSWERS:
Question 1
Using the information above, choose the correct conclusion that interprets the results within the context of the hypothesis test.
- We should reject the null hypothesis because t0<tα. So, at the 10%significance level, the data provide sufficient evidence to conclude that the average percentage of tips received by wait staff in Chicago restaurants is less than 15%.
- We should not reject the null hypothesis because t0<tα. So, at the 10%significance level, the data do not provide sufficient evidence to conclude that the average percentage of tips received by wait staff in Chicago restaurants is less than 15%.
- We should reject the null hypothesis because t0>tα. So, at the 10%significance level, the data provide sufficient evidence to conclude that the average percentage of tips received by wait staff in Chicago restaurants is less than 15%.
- We should not reject the null hypothesis because t0>tα. So, at the 10%significance level, the data do not provide sufficient evidence to conclude that the average percentage of tips received by wait staff in Chicago restaurants is less than 15%.
Answer
We should not reject the null hypothesis because t0>tα. So, at the 10% significance level, the data do not provide sufficient evidence to conclude that the average percentage of tips received by wait staff in Chicago restaurants is less than 15%.
Question 2
Olivia gathered data on the average percentage of tips received by wait staff in 31 restaurants in Chicago. She works through the testing procedure:
- H0:μ=15; Ha: μ<15
- α=0.10(significance level)
- The test statistic is t0 = (x¯−μ0) / s/√ = −1.16.
- The critical value is −t10=−1.310.
Conclude whether to reject or not reject H0. Select two responses below.
Reject H0.
Fail to reject H0.
The test statistic falls within the rejection region.
The test statistic is not in the rejection region.
Answer
Fail to reject H0.
The test statistic is not in the rejection region.
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