Exam 12: Tests of Hypotheses: Means

If hypotheses are $H_{0}: \mu=50 ; H_{A}: \mu \neq 50$ with a sample size of 36 and $s=4$ , find the critical value of $x$ necessary to reject $H_{0}$ for $\alpha=0.02$ .

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 $98 \%$ 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?

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. -Conduct the hypothesis test using $\alpha=0.05$ .

An employment agency wants to estimate the average number of people who will respond to one of their ads. If $\sigma=40$ people, how large a sample is needed to be able to assert with probability 0.95 that the estimate will be off by at most 10 people?

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. -Find a $98 \%$ confidence interval for the true average customer waiting time.

In a one-tailed test that a population mean is at least 50, the alternative hypothesis can be written in symbols as __________.

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. -Find the value of $\bar{x}$ necessary to reject the null hypothesis.

In the hypothesis tests for large and small sample means and differences between means, the left hand term in the numerator is always a population value.

In conducting a hypothesis test, the procedure always assumes that

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, explain under what condition a Type II error would be committed.

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. -Find a $90 \%$ confidence interval for the true average customer waiting time.

In a hypothesis test that a population mean is at least 50, it is a Type I error to conclude that the mean is

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. -Test the hypothesis using the $5 \%$ significance level.

If we increase the confidence level, then we decrease the width of the interval.

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 $8 \mathrm{~m} . p . g$ . -Conduct the hypothesis test if $\alpha=0.01$ .

A housing developer suspects that housing prices in a geographical area are higher than the national average. -If the developer decides to build the community and the survey of housing prices does not produce an average significantly lower than the national average, what hypothesis and alternative should he set up?

The larger the sample size $n$ , the smaller the maximum error of estimate.

A motor vehicle bureau claims that the mean time it takes an arriving applicant to obtain a new registration is 30 minutes. If, as suspected, this figure is too low, what null and alternative hypotheses should be used to put this to the test?

In a test that a difference of two population means is equal to 5, the alternative hypothesis can be written in symbols as __________.

In a hypothesis test, $\alpha$ indicates