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.

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

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 $\alpha=0.05$.

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

A politician claims that he is supported by a clear majority of voters. In a recent survey, 24 out of 40 randomly selected voters indicated that they would vote for the politician. Is the politician's claim justified at the $5 \%$ level of significance?

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.

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 machine that is programmed to package $1.20$ pounds of cereal in each cereal box is being tested for its accuracy. In a sample of 36 cereal boxes, the mean and the standard deviation are calculated as $1.22$ pounds and $0.06$ pound, respectively.

c. At the $5 \%$ level of significance, can you conclude that the machine is working improperly? Explain.

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

A machine that is programmed to package $1.20$ pounds of cereal is being tested for its accuracy. In a sample of 36 cereal boxes, the sample mean filling weight is calculated as $1.22$ pounds. The population standard deviation is known to be $0.06$ pound.

a. Identify the relevant parameter of interest for these quantitative data and compute its point estimate as well as the margin of error with $95 \%$ confidence.

b. Can we conclude that the packaging machine is operating improperly?

c. How large a sample must we take if we want the margin of error to be at most $0.01$ pound with $95 \%$ confidence?

A machine that is programmed to package $1.20$ pounds of cereal is being tested for its accuracy. In a sample of 36 cereal boxes, the sample mean filling weight is calculated as $1.22$ pounds. The population standard deviation is known to be $0.06$ pound.

c. How large a sample must we take if we want the margin of error to be at most $0.01$ pound with $95 \%$ confidence?

A machine that is programmed to package 1,20 pounds of cereal in each cereal box is being tested for its accuracy. In a sample of 36 cereal boxes, the mean and the standard deviation are calculated as $1.22$ pounds and $0.06$ pound, respectively.

a. Set up the null and the alternative hypotheses to determine if the machine is working improperly-that is, it is either underfilling or overfilling the cereal boxes.

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

c. At the $5 \%$ level of significance, can you conclude that the machine is working improperly? Explain.

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?