Exam 12: Tests of Hypotheses: Means

An automobile rustproofing company claims that their methods protect cars for 60 months. This hypothesis is tested against the alternative that the protection lasts for less than 60 months. A random sample of 100 cars produces an average time of 57 months with a standard deviation of 15 months. -State the hypothesis in symbols.

An automobile manufacturer has claimed that his car averages at least $30 \mathrm{~m}$ .p.g. on the highway. A random sample of 16 such cars finds an average of $25 \mathrm{~m}$ . p.g. with a standard deviation of $8 \mathrm{~m} . p . g$ . -State the hypotheses symbolically for the one-tailed test.

A housing developer suspects that housing prices in a geographical area are higher than the national average. Suppose the average national home price is $\$ 64,000$ with a standard deviation of $\$ 5,000$ , and the developer decides to build the community only if, in a random sample of 50 newly -sold houses, the average price is more than $\$ 66,000$ . -What is the probability of the developer not building the community if the area price average is $\$ 67,000$ ?

A housing developer suspects that housing prices in a geographical area are higher than the national average. -If the developer decides to build a housing community only if a survey of housing prices in the area confirms his suspicions, what hypothesis and alternative should he set up?

A sample size of 14 is used to find a confidence interval. The number of degrees of freedom needed is __________.

The probability of a Type I error is equal to __________.

Increasing the sample size increases the probability of making a Type I error.

A bank would like to evaluate whether there is a difference in the effectiveness in the methods they use to teach their management trainees. For 10 employees that are taught by method 1, the average score on an evaluation examination was 86 with a standard deviation of 6 . For 12 employees taught by method 2 , the average score was 81 with a standard deviation of 4. -State the hypotheses for the two-tailed test in symbols.

A college food service wanted to determine whether male students consumed more pizza during a given week than female students. A sample of 60 male students found an average consumption of 48 ounces with a standard deviation of 30 ounces. A sample of 80 female students finds an average consumption of 25 ounces with a standard deviation of 20 ounces. Test the appropriate hypothesis at the 0.01 significance level.

The given confidence level is substituted into the formula used to obtain the required sample size.

We would like to estimate the average amount of time that all students at a certain college spent studying during Spring Weekend. We would like to be $\mathbf{9 0} \%$ confident that our estimate is within .5 hours of the actual population average. -Find the minimum number of students that need to be sampled if it is known that the maximum and minimum amounts of hours were done by students who studied for 15 hours and 0 hours respectively.

We would like to estimate the average amount of time that all students at a certain college spent studying during Spring Weekend. We would like to be $\mathbf{9 0} \%$ confident that our estimate is within .5 hours of the actual population average. -Find a $90 \%$ confidence interval for the average study time of all students at the college if the sample average was 3.5 hours.

Two supermarket owners each claim that more customers enter their store than enter the other's store. A survey was taken and it was found that in 60 days an average of 810 people per day entered the first store with a standard deviation of 40 people. A corresponding survey found that in 80 days an average of 800 people per day entered the second store with a standard deviation of 30 people. -For the above situation, conduct the two-tailed test with $\alpha=0.05$ .

A manager of a cafeteria wants to estimate the average time customers wait before being served. A random sample of 49 customers has an average waiting time of 8.4 minutes with a standard deviation of 3.5 minutes. -With $90 \%$ confidence, what can the manager conclude about the possible size of his error in using 8.4 minutes to estimate the true average waiting time?

The alternative hypothesis can never contain an equal sign.