Research commissioned by Vodafone suggests that older workers are the happiest employees (BBC News, July 21, 2008). The report documents that $70 \%$ of older workers in England feel fulfilled, compared with just $50 \%$ of younger workers. A demographer believes that an identical pattern does not exist in Asia. A survey of 120 older workers in Asia finds that 75 feel fulfilled. A similar survey finds that $58 \%$ of 210 younger workers feel fulfilled.

a. At the $5 \%$ level of significance, test if older workers in Asia feel less fulfilled than their British counterparts.

b. At the $5 \%$ level of significance, test if younger workers in Asia feel more fulfilled than their British counterparts.

A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. For this to happen, it will have to move one of its most viewed shows to another slot. The network conducts a survey asking its viewers which show they would rather watch. The network will keep its current lineup of shows unless the majority of the customers want to watch the new show. The network receives 827 responses, of which 428 indicate that they would like to see the new show in the lineup.

c. At $\alpha=0.01$, what should the television network do?

A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. For this to happen, it will have to move one of its most viewed shows to another slot. The network conducts a survey asking its viewers which show they would rather watch. The network will keep its current lineup of shows unless the majority of the customers want to watch the new show. The network receives 827 responses, of which 428 indicate that they would like to see the new show in the lineup.

b. Calculate the value of the test statistic and the $p$-value.

The table shows the average prices (in dollars) of jeans sold at different stores and the numbers of pairs of jeans sold at each store in one month. Is there a relationship between the average price and the number sold? Explain your reasoning.

$$\begin{matrix} \text{Average Price (dollars)} & \text{22} & \text{40} & \text{28} & \text{35} & \text{46}\\ \text{Number Sold} & \text{152} & \text{94} & \text{134} & \text{110} & \text{81}\\ \end{matrix}$$

Consider the following hypotheses:

$$\begin{aligned} &H_0: \mu \geq 150 \\ &H_A: \mu<150 \end{aligned}$$

b. Does the above sample evidence enable us to reject the null hypothesis at $\alpha=0.01$ ?

A car manufacturer is trying to develop a new sports car. Engineers are hoping that the average amount of time that the car takes to go from 0 to 60 miles per hour is below 6 seconds. The manufacturer tested 12 of the cars and clocked their performance times. Three of the cars clocked in at $5.8$ seconds, 5 cars at $5.9$ seconds, 3 cars at $6.0$ seconds, and 1 car at $6.1$ seconds. At the $5 \%$ level of significance, test if the new sports car is meeting its goal to go from 0 to 60 miles per hour in less than 6 seconds. Assume a normal distribution for the analysis.

Consider the following hypotheses:

$$\begin{aligned} &H_0: \mu \leq 210 \\ &H_A: \mu>210 \end{aligned}$$

Find the $p$-value for this test based on the following sample information.

b. $\bar{X}=216 ; s=26 ; n=80$

Consider the following hypotheses:

$$\begin{aligned} &H_0: p=0.32 \\ &H_A: p \neq 0.32 \end{aligned}$$

Calculate the $p$-value based on the following sample information a. $x=20 ; n=66$

b. $x=100 ; n=264$

c. $\bar{p}=0.40 ; \mathrm{n}=40$

d. $\bar{p}=0.38 ; n=180$

In order to conduct a hypothesis test for the population proportion, you sample 320 observations that result in 128 successes. Conduct the following tests at $\alpha=0.05$.

a. $H_0: p \geq 0.45 ; H_A: p<0.45$

b. $H_0: p=0.45 ; H_A: p \neq 0.45$

A realtor in Mission Viejo, California, believes that the average price of a house is more than 500,000$.

a. State the null and the alternative hypotheses for the test.

b. The data accompanying this exercise show house prices. (Data are in 1,000$ s.) Use Excel's Z.TEST function to calculate the $p$-value. Assume the population standard deviation is $\$ 100$ (in 1,000$s).

c. At$\alpha=0.05$, what is the conclusion to the test? Is the realtor's claim supported by the data?

A realtor in Mission Viejo, California, believes that the average price of a house is more than $\$ 500,000$.

b. The data accompanying this exercise show house prices. (Data are in $\$ 1,000 \mathrm{~s}$.) Assume the population standard deviation is $\$ 100$ (in $\$ 1,000$ s). What is the value of the test statistic and the $p$-value?

A realtor in Mission Viejo, California, believes that the average price of a house is more than $\$ 500,000$.

c. At $\alpha=0.05$, what is the conclusion to the test? Is the realtor's claim supported by the data?

A realtor in Mission Viejo, California, believes that the average price of a house is more than $\$ 500,000$.

a. State the null and the altemative hypotheses for the test.

b. The data accompanying this exercise show house prices. (Data are in $\$ 1,000 \mathrm{~s}$.) Assume the population standard deviation is $\$ 100$ (in $\$ 1,000$ s). What is the value of the test statistic and the $p$-value?

c. At $\alpha=0.05$, what is the conclusion to the test? Is the realtor's claim supported by the data?

A realtor in Mission Viejo, California, believes that the median price of a house is more than $\$ 500,000$.

a. Specify the competing hypotheses for the test.

b. Using the $\boldsymbol{M} \boldsymbol{V}_{-}$Houses data, calculate the value of the test statistic. Assume the normal approximation for $T$.

c. Calculate the $p$-value.

d. At the $5 \%$ significance level, is the realtor's claim supported by the data?