Software analysis of the salaries of a random sample of 288 Nevada teachers produced the confidence interval shown below. Which conclusion is correct? What’s wrong with the others?

$$\text { t-Inter val for } \mu : \left. \begin{array} { c c } { \text {with } 90.00 \% \text { Confidence, } } \\ { } { 38944 < \mu [ \text { TchPay]} < 42893 } \end{array} \right.$$

a) If we took many random samples of 288 Nevada teachers, about 9 out of 10 of them would produce this confidence interval. b) If we took many random samples of Nevada teachers, about 9 out of 10 of them would produce a confidence interval that contained the mean salary of all Nevada teachers. c) About 9 out of 10 Nevada teachers earn between $38,944 and$42,893. d) About 9 out of 10 of the teachers surveyed earn between $38,944 and$42,893. e) We are 90% confident that the average teacher salary in the United States is between $38,944 and$42,893.

The housing market has recovered slowly from the economic crisis of 2008. Recently, in one large community, realtors randomly sampled 36 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss was $9,560 with a standard deviation of$1500. a) What assumptions and conditions must be checked before finding a confidence interval? How would you check them? b) Find a 95% confidence interval for the mean loss in value per home. c) Interpret this interval and explain what 95% confidence means in this context.

Software analysis of the salaries of a random sample of 288 Nevada teachers produced the confidence interval shown below. Which conclusion is correct? What's wrong with the others?

$$\begin{array}{l}\text { t-Interval with } 90.00 \% \text { confidence, } \\ \text { for } \mu: \quad \$ 53159<\mu(\text { T ch pay })<\$ 58755\end{array}$$

a) If we took many random samples of 288 Nevada teachers, about 9 out of 10 of them would produce this confidence interval. b) If we took many random samples of Nevada teachers, about 9 out of 10 of them would produce a confidence interval that contained the mean salary of all Nevada teachers. c) About 9 out of 10 Nevada teachers earn between $53,159 and$58,755. d) About 9 out of 10 of the teachers surveyed earn between $53,159 and$58,755. e) We are 90% confident that the average teacher salary in the United States is between $53,159 and$58,755.

Software analysis of the salaries of a random sample of 288 Nevada teachers produced the confidence interval shown below. Which conclusion is correct? What's wrong with the others? t-Interval for

$$\mu$$

: with 90.00 % Confidence, 38944 <

$$\mu$$

(TchPay) < 42893. If we took many random samples of Nevada teachers, about 9 out of 10 of them would produce a confidence interval that contained the mean salary of all Nevada teachers.

Software analysis of the salaries of a random sample of 288 Nevada teachers produced the confidence interval shown below. Which conclusion is correct? What's wrong with the others? t-Interval for

$$\mu$$

: with 90.00 % Confidence, 38944 <

$$\mu$$

(TchPay) < 42893. If we took many random samples of 288 Nevada teachers, about 9 out of 10 of them would produce this confidence interval.

A medical researcher measured the pulse rates (beats per minute) of a sample of randomly selected adults and found the following Student 's t-based confidence interval:

$$\left. \begin{array} { c } { \text { With } 95.00 \% \text { Confidence, } } \\ { 70.887604 < \mu ( \text { Pulse } ) < 74.497011 } \end{array} \right.$$

Explain carefully what the software output means.

In the previous exercise, you found a 95% confidence interval to estimate the average loss in home value.

Suppose the standard deviation of the losses had been $3000 instead of$1500. What would the larger standard deviation do to the width of the confidence interval (assuming the same level of confidence)?

After surveying students at Dartmouth College, a campus organization calculated that a 95% confidence interval for the mean cost of food for one term (of three in the Dartmouth trimester calendar) is ($1372,$1562). Now the organization is trying to write its report and is considering the following interpretations. Comment on each. a) 95% of all students pay between $1372 and$1562 for food. b) 95% of the sampled students paid between $1372 and$1562. c) We're 95% sure that students in this sample averaged between $1372 and$1562 for food. d) 95% of all samples of students will have average food costs between $1372 and$1562. e) We're 95% sure that the average amount all students pay is between $1372 and$1562.

A nutrition lab tested 40 hot dogs to see if their mean sodium content was less than the 325-mg upper limit set by regulations for "reduced sodium" franks. The lab failed to reject the hypothesis that the hot dogs did not meet this requirement, with a P-value of 0.142. A 90% confidence interval estimated the mean sodium content for this kind of hot dog at 317.2 to 326.8 mg. Explain how these two results are consistent. Your explanation should discuss the confidence level, the P-value, and the decision.

A researcher tests whether the mean cholesterol level among those who eat frozen pizza exceeds the value considered to indicate a health risk. She gets a P-value of 0.07. Explain in this context what the "7%" represents.

Software analysis of the salaries of a random sample of 288 Nevada teachers produced the confidence interval shown below. Which conclusion is correct? What's wrong with the others? t-Interval for

$$\mu$$

: with 90.00 % Confidence, 38944 <

$$\mu$$

(TchPay) < 42893. About 9 out of 10 Nevada teachers earn between $38,944 and$42,893..

Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure through parking fees. During a two-month period (44 weekdays), daily fees collected averaged $126, with a standard deviation of$15. a) What assumptions must you make in order to use these statistics for inference? b) Write a 90% confidence interval for the mean daily income this parking garage will generate. c) Interpret this confidence interval in context. d) Explain what “90% confidence” means in this context. e) The consultant who advised the city on this project predicted that parking revenues would average $130 per day. Based on your confidence interval, do you think the consultant was correct? Why?

In 1998, as an advertising campaign, the Nabisco Company announced a “1000 Chips Challenge,” claiming that every 18-ounce bag of their Chips Ahoy cookies contained at least 1000 chocolate chips. Dedicated Statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies, and counted the chocolate chips. Some of their data are given below.

$$\left. \begin{array} { c c c } { 1219 } & { 1214 } & { 1087 } & { 1200 } & { 1419 } & { 1121 } & { 1325 } & { 1345 } \\ { 1244 } & { 1258 } & { 1356 } & { 1132 } & { 1191 } & { 1270 } & { 1295 } & { 1135 } \end{array} \right.$$

a) Check the assumptions and conditions for inference. Comment on any concerns you have. b) Create a 95% confidence interval for the average number of chips in bags of Chips Ahoy cookies. c) What does this evidence say about Nabisco’s claim? Use your confidence interval to test an appropriate hypothesis and state your conclusion.

Based on meteorological data for the past century, a local TV weather forecaster estimates that the region's average winter snowfall is 23", with a margin of error of

$${\pm}2$$

inches. Assuming he used a 95% confidence interval, how should viewers interpret this news? Comment on each of these statements:

During 95 of the past 100 winters, the region got between 21" and 25" of snow.