The Mean Corporation would like to invest in the booming health food industry. It is considering the creation of a health-drink franchise called Goose Juice. The investment department of the Mean Corporation wants to investigate the feasibility of this venture by examining the profits of similar franchises. It believes that the venture will be feasible if an average annual profit of more than $73,000 can be expected from each Goose Juice that is opened. It is known that the annual profits earned by health-drink franchises has a population standard deviation of $8,400.

The Mean Corporation's statisticians would like to construct a hypothesis test for the mean annual profit () earned by health-drink franchises. A random sample of 20 franchises were chosen and their annual profit for the previous financial year was recorded. The mean annual profit for the sample was calculated as $74,800. The hypotheses that will be used by the statisticians areH₀: = 73,000andH_A: > 73,000.

You may find thisstandard normal tableuseful throughout the following questions.

a)Calculate the test statistic (z) that corresponds to the sample and hypotheses. Give your answer to 3 decimal places.

z =

b)Using the test statistic for the Mean Corporation's hypothesis test and level = 0.05, the Mean Corporation shouldacceptrejectnot rejectthe null hypothesis.

c)If the sample size is increased to 83 (but the sample mean remains unchanged), the Mean Corporation shouldacceptrejectnot rejectthe null hypothesis.

A consumer watchdog is monitoring the Myths chip company. In particular, they are suspicious about the net weight of chips in the company's 2 ounce chip bags. They decide that they will have enough evidence to take action if they can conclude that the mean weight of these chip bags () is less than 2 ounces. A hypothesis test is conducted with the following hypotheses:

H₀: = 2

H_A: < 2

The level of significance used in this test is = 0.05. A random sample of 26 chip bags are collected and weighed. The sample mean weight is calculated to bex= 1.91and the sample standard deviation iss = 0.29. You may find thisStudent's t distribution tableuseful throughout this question.

a)Calculate the test statistic (t) for this test. Give your answer to 4 decimal places.

t =

b)The result of this test is that the null hypothesisisis notrejected.

The government of Preon (a small island nation) was voted in at the last election with 66% of the votes. That was 2 years ago, and ever since then the government has assumed that their approval rating has been the same. Some recent events have affected public opinion and the government suspects that their approval rating might have changed. They decide to run a hypothesis test for the proportion of people who would still vote for them.

The null and alternative hypotheses are:

H₀:= 0.66

H_A: 0.66

The level of significance used in the test is = 0.025. A random sample of 113 people are asked whether or not they would still vote for the government. The proportion of people that would is equal to 0.770. You may find thisstandard normal tableuseful throughout this question.

a)Calculate the test statistic (z) for this hypothesis test. Give your answer to 3 decimal places.

z =

b)According to this test statistic, you shouldacceptrejectnot rejectthe null hypothesis.