Staistic

1. Test the claim that the mean GPA of night students is significantly different than 2.5 at the 0.05 significance level. The null and alternative hypothesis would be:

---------------------- ------------------------------ --------------------------------

The test is:

left-tailed

two-tailed

right-tailed

Based on a sample of 20 people, the sample mean GPA was 2.54 with a standard deviation of 0.05 The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals) Based on this we:

· Reject the null hypothesis

· Fail to reject the null hypothesis

2. Test the claim that the mean GPA of night students is smaller than 2.5 at the 0.01 significance level. The null and alternative hypotheses would be:

Based on a sample of 34 people, the sample mean GPA was 2.46 with a standard deviation of 0.06 The p-value is: (to 3 decimals) The significance level is: (to 2 decimals) Based on this we:

· Fail to reject the null hypothesis

· Reject the null hypothesis

3. Test the claim that the mean GPA of night students is larger than 3.4 at the .10 significance level. The null and alternative hypothesis would be:

The test is:

left-tailed

right-tailed

two-tailed

Based on a sample of 75 people, the sample mean GPA was 3.43 with a standard deviation of 0.07 The test statistic is: (to 2 decimals) The critical value is: (to 2 decimals) Based on this we:

· Fail to reject the null hypothesis

· Reject the null hypothesis

4. Currently patrons at the library speak at an average of 60 decibels. Will this average change after the installation of a new computer plug in station? After the plug in station was built, the librarian randomly recorded 56 people speaking at the library. Their average decibel level was 64.1 and their standard deviation was 19. What can be concluded at the the  = 0.01 level of significance?

· For this study, we should use ___________________

· The null and alternative hypotheses would be: ___________________

5. As part of your work for an environmental group, you want to see if the mean amount of waste generated per adult in your community is less than the national average of 5 pounds per day. You take a simple random sample of 28 adults in your community and find that they average 4.7 pounds with a standard deviation of 1.4 pounds. Suppose you know the amount of waste generated per day follows a normal distribution. Test at .05 significance. Round to the fourth as needed We can work this problem because:

SRS IS GIVEN_______________________

H0:______ ________

Ha:_______ _____

Test Statistic: P-value: Did something significant happen? Select the Decision Rule:

There ____________enough evidence to conclude

6. The average student-loan debt is reported to be $25,235. A student believes that the student-loan debt is higher in her area. She takes a random sample of 100 college students in her area and determines the mean student-loan debt is $27,524 and the standard deviation is $6,000. Is there sufficient evidence to support the student's claim at a 5% significance level?

Preliminary:

a. Is it safe to assume that 

  of all college students in the local area?

· No

· Yes

 Is  ?

· No

· Yes

  Test the claim:

a. Determine the null and alternative hypotheses. Enter correct symbol and value.

: :



 Determine the test statistic. Round to two decimals.



 Find the -value. Round to 4 decimals.

 -value =

 Make a decision.

· Fail to reject the null hypothesis.

· Reject the null hypothesis.

 Write the conclusion.

· There is not sufficient evidence to support the claim that student-loan debt is higher than $25,235 in her area.

· There is sufficient evidence to support the claim that student-loan debt is higher than $25,235 in her area.

7. The work week for adults in the US that work full time is normally distributed with a mean of 47 hours. A newly hired engineer at a start-up company believes that employees at start-up companies work more on average then most working adults in the US. She asks 12 engineering friends at start-ups for the lengths in hours of their work week. Their responses are shown in the table below. Test the claim using a 10% level of significance. Give answer to at least 4 decimal places.

Hours
47
49
53
50
49
64
60
52
47
48
51
52

a. What are the correct hypotheses? 

H0:

hours H1:

hours

Based on the hypotheses, find the following: b. Test Statistic = c. p-value =

d. The correct decision is to

.

e. The correct summary would be:

that the mean number of hours of all employees at start-up companies work more than the US mean of 47 hours.

8. The average wait time to get seated at a popular restaurant in the city on a Friday night is 11 minutes.  Is the mean wait time greater for men who wear a tie? Wait times for 15 randomly selected men who were wearing a tie are shown below. Assume that the distribution of the population is normal.

12, 12, 11, 13, 11, 10, 12, 11, 11, 13, 10, 11, 10, 10, 9

What can be concluded at the the 

= 0.10 level of significance level of significance?

a. For this study, we should use

1. The null and alternative hypotheses would be:     

 

  

    

 

  

 

c. The test statistic

 = (please show your answer to 3 decimal places.)

 The p-value = (Please show your answer to 4 decimal places.)

 The p-value is Based on this, we should

 the null hypothesis.

 Thus, the final conclusion is that ...

· The data suggest the populaton mean is significantly more than 11 at

 = 0.10, so there is statistically significant evidence to conclude that the population mean wait time for men who wear a tie is more than 11.

 The data suggest that the population mean wait time for men who wear a tie is not significantly more than 11 at

 = 0.10, so there is statistically insignificant evidence to conclude that the population mean wait time for men who wear a tie is more than 11.

 The data suggest the population mean is not significantly more than 11 at

1.

0. = 0.10, so there is statistically insignificant evidence to conclude that the population mean wait time for men who wear a tie is equal to 11.

9. The average salary in this city is $43,100. Is the average less for single people? 61 randomly selected single people who were surveyed had an average salary of $39,913 and a standard deviation of $9,290.  What can be concluded at the  

= 0.01 level of significance? 

a. For this study, we should use

1. The null and alternative hypotheses would be:     

 

  

    

 

  

 

c. The test statistic

 = (please show your answer to 3 decimal places.)

 The p-value = (Please show your answer to 4 decimal places.)

 The p-value is Based on this, we should

 the null hypothesis.

 Thus, the final conclusion is that ...

· The data suggest that the sample mean is not significantly less than 43,100 at

 = 0.01, so there is statistically insignificant evidence to conclude that the sample mean salary for singles is less than 39,913.

 The data suggest that the population mean is not significantly less than 43,100 at

 = 0.01, so there is statistically insignificant evidence to conclude that the population mean salary for singles is less than 43,100.

 The data suggest that the populaton mean is significantly less than 43,100 at

·  = 0.01, so there is statistically significant evidence to conclude that the population mean salary for singles is less than 43,100.

 Interpret the p-value in the context of the study.

· If the population mean salary for singles is $43,100 and if another 61 singles are surveyed then there would be a 0.47551077% chance that the population mean salary for singles would be less than $43,100.

· There is a 0.47551077% chance that the population mean salary for singles is less than $43,100.

· There is a 0.47551077% chance of a Type I error.

· If the population mean salary for singles is $43,100 and if another 61 singles are surveyed then there would be a 0.47551077% chance that the sample mean for these 61 singles surveyed would be less than $39,913.

 Interpret the level of significance in the context of the study.

· If the population mean salary for singles is $43,100 and if another 61 singles are surveyed then there would be a 1% chance that we would end up falsely concluding that the population mean salary for singles is less than $43,100.

· There is a 1% chance that you won the lottery, so you may not have to even have to worry about passing this class.

· There is a 1% chance that the population mean salary for singles is less than $43,100.

· If the population population mean salary for singles is less than $43,100 and if another 61 singles are surveyed then there would be a 1% chance that we would end up falsely concluding that the population mean salary for singles is equal to $43,100.

10. The average salary for American college graduates is $49,700. You suspect that the average is more for graduates from your college. The 64 randomly selected graduates from your college had an average salary of $50,000 and a standard deviation of $8,010. What can be concluded at the  

= 0.10 level of significance?

a. For this study, we should use

1. The null and alternative hypotheses would be:     

 

  

    

 

  

 

c. The test statistic

 = (please show your answer to 4 decimal places.)

 The p-value = (Please show your answer to 4 decimal places.)

 The p-value is Based on this, we should

 the null hypothesis.

 Thus, the final conclusion is that ...

· The data suggest that the populaton mean is significantly greater than 49,700 at

 = 0.10, so there is statistically significant evidence to conclude that the population mean salary for graduates from your college is greater than 49,700.

 The data suggest that the population mean is not significantly greater than 49,700 at

 = 0.10, so there is statistically insignificant evidence to conclude that the population mean salary for graduates from your college is greater than 49,700.

 The data suggest that the sample mean is not significantly greater than 49,700 at

·  = 0.10, so there is statistically insignificant evidence to conclude that the sample mean salary for graduates from your college is greater than 50,000.

 Interpret the p-value in the context of the study.

· There is a 38.25729249% chance that the population mean salary for graduates from your college is greater than $49,700 .

· If the population mean salary for graduates from your college is $49,700 and if another 64 graduates from your college are surveyed then there would be a 38.25729249% chance that the population mean salary for graduates from your college would be greater than $49,700.

· There is a 38.25729249% chance of a Type I error.

· If the population mean salary for graduates from your college is $49,700 and if another 64 graduates from your college are surveyed then there would be a 38.25729249% chance that the sample mean for these 64 graduates from your college surveyed would be greater than $50,000.

 Interpret the level of significance in the context of the study.

· If the population mean salary for graduates from your college is $49,700 and if another 64 graduates from your college are surveyed then there would be a 10% chance that we would end up falsely concluding that the population mean salary for graduates from your college is greater than $49,700.

· There is a 10% chance that the population mean salary for graduates from your college is greater than $49,700.

· There is a 10% chance that your won't graduate, so what's the point?

· If the population population mean salary for graduates from your college is greater than $49,700 and if another 64 graduates from your college are surveyed then there would be a 10% chance that we would end up falsely concluding that the population mean salary for graduates from your college is equal to $49,700.

11. Women are recommended to consume 1830 calories per day. You suspect that the average calorie intake is different for women at your college. The data for the 14 women who participated in the study is shown below:

1880, 1756, 1813, 1834, 1707, 1547, 1947, 1528, 1552, 1723, 1634, 1541, 1639, 1608

Assuming that the distribution is normal, what can be concluded at the 

= 0.05 level of significance?

a. For this study, we should use

1. The null and alternative hypotheses would be:     

 

  

    

 

  

 

c. The test statistic

 = (please show your answer to 3 decimal places.)

 The p-value = (Please show your answer to 4 decimal places.)

 The p-value is Based on this, we should

 the null hypothesis.

 Thus, the final conclusion is that ...

· The data suggest that the population mean calorie intake for women at your college is not significantly different from 1830 at

 = 0.05, so there is insufficient evidence to conclude that the population mean calorie intake for women at your college is different from 1830.

 The data suggest the populaton mean is significantly different from 1830 at

 = 0.05, so there is sufficient evidence to conclude that the population mean calorie intake for women at your college is different from 1830.

 The data suggest the population mean is not significantly different from 1830 at

1.

0. = 0.05, so there is sufficient evidence to conclude that the population mean calorie intake for women at your college is equal to 1830.

1. Interpret the p-value in the context of the study.

1. There is a 0.25305142% chance of a Type I error.

1. There is a 0.25305142% chance that the population mean calorie intake for women at your college is not equal to 1830.

1. If the population mean calorie intake for women at your college is 1830 and if you survey another 14 women at your college then there would be a 0.25305142% chance that the population mean would either be less than 1967 or greater than 1694.

1. If the population mean calorie intake for women at your college is 1830 and if you survey another 14 women at your college, then there would be a 0.25305142% chance that the sample mean for these 14 women would either be less than 1967 or greater than 1694.

1. Interpret the level of significance in the context of the study.

2. There is a 5% chance that the women at your college are just eating too many desserts and will all gain the freshmen 15.

2. There is a 5% chance that the population mean calorie intake for women at your college is different from 1830.

2. If the population mean calorie intake for women at your college is different from 1830 and if you survey another 14 women at your college, then there would be a 5% chance that we would end up falsely concuding that the population mean calorie intake for women at your college is equal to 1830.

2. If the population mean calorie intake for women at your college is 1830 and if you survey another 14 women at your college, then there would be a 5% chance that we would end up falsely concuding that the population mean calorie intake for women at your college is different from 1830.

12. The average house has 11 paintings on its walls.  Is the mean larger for houses owned by teachers? The data show the results of a survey of 12 teachers who were asked how many paintings they have in their houses. Assume that the distribution of the population is normal.

14, 13, 12, 10, 14, 13, 14, 10, 12, 11, 13, 14

What can be concluded at the  

= 0.05 level of significance?

a. For this study, we should use

1. The null and alternative hypotheses would be:     

 

  

    

 

  

 

c. The test statistic

 = (please show your answer to 3 decimal places.)

 The p-value = (Please show your answer to 4 decimal places.)

 The p-value is Based on this, we should

 the null hypothesis.

 Thus, the final conclusion is that ...

· The data suggest that the population mean number of paintings that are in teachers' houses is not significantly more than 11 at

 = 0.05, so there is insufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is more than 11.

 The data suggest the population mean is not significantly more than 11 at

 = 0.05, so there is sufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is equal to 11.

 The data suggest the populaton mean is significantly more than 11 at

1.

0. = 0.05, so there is sufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is more than 11.

1. Interpret the p-value in the context of the study.

1. There is a 0.27% chance that the population mean number of paintings that are in teachers' houses is greater than 11.

1. If the population mean number of paintings that are in teachers' houses is 11 and if you survey another 12 teachers then there would be a 0.27% chance that the population mean number of paintings that are in teachers' houses would be greater than 11.

1. There is a 0.27% chance of a Type I error.

1. If the population mean number of paintings that are in teachers' houses is 11 and if you survey another 12 teachers then there would be a 0.27% chance that the sample mean for these 12 teachers would be greater than 12.5.

1. Interpret the level of significance in the context of the study.

2. There is a 5% chance that the population mean number of paintings that are in teachers' houses is more than 11.

2. There is a 5% chance that teachers are so poor that they are all homeless.

2. If the population mean number of paintings that are in teachers' houses is 11 and if you survey another 12 teachers, then there would be a 5% chance that we would end up falsely concuding that the population mean number of paintings that are in teachers' houses is more than 11.

2. If the population mean number of paintings that are in teachers' houses is more than 11 and if you survey another 12 teachers, then there would be a 5% chance that we would end up falsely concuding that the population mean number of paintings that are in teachers' houses is equal to 11.