From the earlier exercise in the previous chapter, Bjork Larsen was trying to decide whether to use a new racing wax for cross-country skis. He decided that the wax would be worth the price if he could average less than 55 seconds on a course he knew well, so he planned to study the wax by racing on the course 8 times. His 8 race times were 56.3, 65.9, 50.5, 52.4, 46.5, 57.8, 52.2, and 43.2 seconds. Should he buy the wax? Explain by performing an appropriate hypothesis test.

We saw from the earlier exercise in the previous chapter, that some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5.

Find the mean and standard deviation of the weights.

We saw from the earlier exercise in the previous chapter, that some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5.

Do these data satisfy the assumptions for inference? Explain.

Referring to the study of the earlier exercise:

a) Is the alternative to the null hypothesis more naturally onesided or two-sided? Explain.

b) The P-value from a clinical trial testing the hypothesis is 0.0028. What do you conclude?

c) What would you have concluded if the P-value had been 0.28?

For each of the following situations, define the parameter and write the null and alternative hypotheses in terms of parameter values.

Regular card customers have been with the company for an average of 15.2 months. The credit card bank wants to know if their Gold card customers have been with the company on average the same amount of time.

Many people have trouble setting up all the features of their smartphones, so a company has developed what it hopes will be easier instructions. The goal is to have at least 96% of customers succeed. The company tests the new system on 200 people, of whom 188 were successful. Is this strong evidence that the new system fails to meet the company's goal? A student 's test of this hypothesis is shown. How many mistakes can you find?

$$\left. \begin{array} { l } { \mathrm { H } _ { 0 } : \hat { p } = 0.96 } \\ { \mathrm { H } _ { \mathrm { A } } : \hat { p } \neq 0.96 } \end{array} \right.$$

,

$$\operatorname { SRS }, 0.96 ( 200 ) > 10$$

,

$$\frac { 188 } { 200 } = 0.94 , \quad S D ( \hat { p } ) = \sqrt { \frac { ( 0.94 ) ( 0.06 ) } { 200 } } = 0.017$$

,

$$z = \frac { 0.96 - 0.94 } { 0.017 } = 1.18$$

,

$$\mathrm { P } = P ( z > 1.18 ) = 0.12$$

There is strong evidence the new instructions don't work.

For each of the following situations, define the parameter and write the null and alternative hypotheses in terms of parameter values.

Regular card customers have a default rate of 2.3 percent. A credit card bank wants to know if that rate is different for their Gold card customers.

For each of the following situations, define the parameter and write the null and alternative hypotheses in terms of parameter values.

Last year, a survey found that 53 percent of the employees were willing to pay for on-site day care. The company wants to know if that has changed.

Recall from the earlier exercise in the previous chapter, that students investigated the packaging of potato chips. They purchased 6 bags of Lay's Ruffles marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.3, 28.2, 29.1, 28.7, 28.9, 28.5.

Test the hypothesis that the net weight is as claimed.

For each of the following situations, define the parameter and write the null and alternative hypotheses in terms of parameter values.

Seat-belt compliance among university students in Kuala Lumpur was 40 percent in 1993 . The city wants to know if it has changed.

Recall from the earlier exercise in the previous chapter, that students investigated the packaging of potato chips. They purchased 6 bags of Lay's Ruffles marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.3, 28.2, 29.1, 28.7, 28.9, 28.5.

Find the mean and standard deviation of the weights.

Recall from the earlier exercise in the previous chapter, that students investigated the packaging of potato chips. They purchased 6 bags of Lay's Ruffles marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.3, 28.2, 29.1, 28.7, 28.9, 28.5.

Do these data satisfy the assumptions for inference? Explain.

The technology committee of the earlier exercise from the previous chapter wants to perform a test to see if the mean amount of time students are spending in the lab has increased from 55 minutes. Here are the data from a random sample of 12 students.

$$\begin{array}{c} \begin{array}{c} \text{Time} \end{array} \\ \begin{array}{l|r} \hline 52 & 74 \\ 57 & 53 \\ 54 & 136 \\ 76 & 73 \\ 62 & 8 \\ 52 & 62 \end{array} \end{array}$$

What do you conclude about the claim? If there are outliers, perform the test with and without the outliers present.

The technology committee of the earlier exercise from the previous chapter wants to perform a test to see if the mean amount of time students are spending in the lab has increased from 55 minutes. Here are the data from a random sample of 12 students.

$$\begin{array}{c} \begin{array}{c} \text{Time} \end{array} \\ \begin{array}{l|r} \hline 52 & 74 \\ 57 & 53 \\ 54 & 136 \\ 76 & 73 \\ 62 & 8 \\ 52 & 62 \end{array} \end{array}$$

Plot the data. Are any of the observations outliers? Explain.