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

An article found that Massachusetts residents spent an average of $\$ 860.70$ on the lottery in 2010, more than three times the U.S. average (www.businessweek.com, March 14, 2012). A researcher at a Boston think tank believes that Massachusetts residents spend less than this amount. He surveys 100 Massachusetts residents and asks them about their annual expenditures on the lottery.

b. Calculate 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 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?

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 police officer is concerned about speeds on a certain section of Interstate $95$. The data accompanying this exercise show the speeds of $40$ cars on a Saturday afternoon.

At $\alpha=0.01$, are the officer's concerns warranted? Explain.

A police officer is concerned about speeds on a certain section of Interstate $95$. The data accompanying this exercise show the speeds of $40$ cars on a Saturday afternoon.

Calculate 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$.

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 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?

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 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.

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

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?