Exam 9: Statistical Inference: Hypothesis Testing for Single Populations

The local oil changing business is very busy on Saturday mornings and is considering expanding.A national study of similar businesses reported the mean number of customers waiting to have their oil changed on Saturday morning is 3.6.Suppose the local oil changing business owner, wants to perform a hypothesis test.The null hypothesis is the population mean is 3.6 and the alternative hypothesis that the population mean is not equal to 3.6.The owner takes a random sample of 16 Saturday mornings during the past year and determines the sample mean is 4.2 and the sample standard deviation is 1.4.It can be assumed that the population is normally distributed.The observed "t" value for this problem is _______.

Suppose you are testing the null hypothesis that a population mean is greater than or equal to 60, against the alternative hypothesis that the population mean is less than 60.The sample size is 64 and $\alpha$ = .05.If the sample mean is 58 and the population standard deviation is 16, the observed z value is _______.

The lifetime of a squirrel follows a normal distribution with mean μ months and a standard deviation $\sigma$ =7 months.To test the alternative hypothesis that μ > 40, 25 squirrels are randomly selected.The null hypothesis is rejected when the sample mean is bigger than 43.Assuming that μ=45, the probability of type II error is approximately _________.

The executives of CareFree Insurance, Inc.feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance.Eighty employees rate the management as participatory.The appropriate decision is to __________.

A company has a contract to supply specialized batteries to a manufacturer with a mean width of 54mm and a standard deviation of 1.5 or less with an alpha of 0.10.The company randomly tests 25 of these batteries to ensure that they are meeting the requirements of the contract.If the most recent test had a standard deviation of 1.8 what would be the observed chi-squared value?

The weight of a USB flash drive is 30 grams and is normally distributed.Periodically, quality control inspectors at Dallas Flash Drives randomly select a sample of 17 USB flash drives.If the mean weight of the USB flash drives is too heavy or too light the machinery is shut down for adjustment; otherwise, the production process continues.The last sample showed a mean and standard deviation of 31.9 and 1.8 grams, respectively.The null hypothesis is ______.

A company has a contract to supply specialized batteries to a manufacturer with a mean width of 54mm and a standard deviation of 1.5 or less with an alpha of 0.10.The company randomly tests 25 of these batteries to ensure that they are meeting the requirements of the contract.If the most recent test had a standard deviation of 1.8 what would be the critical value of this chi-squared test?

A recent survey suggests 30% of boat owners do not regularly use their boat after the second year of ownership.A local boat dealer wants to test the alternative hypothesis that p > .30 with α = .05.He surveys 60 boat owners and finds 42% of the owners who have owned their boat for three years report they do not regularly use their boat.Assuming that p = .35, the probability of type II error is approximately ________.

Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks.One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans.Last Friday's sample contained 30 defaulted loans.Ophelia's null hypothesis is _______.

David Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB.Based on a recent census of personnel, David knows that the variance of teller training time in the southeast region is 8, and he wonders if the variance in the southwest region is the same number.His staff randomly selected personnel files for 15 tellers in the southwest region, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours.Assume that teller training time is normally distributed.Using $\alpha$ = 0.10, the appropriate decision is ________.

The lifetime of a squirrel follows a normal distribution with mean μ = 40 months and a standard deviation $\sigma$ = 7 months.To test the hypothesis that μ > 40, 25 squirrels are randomly selected.Assuming that μ = 45, and α = 0.1, the probability of type II error is approximately

In a two-tailed hypothesis about a population mean with a sample size of 100, $\sigma$ is known, and α = 0.05, the rejection region would be _______.

A researcher is testing a hypothesis of a single mean.The critical z value for $\alpha$ = .05 in a two-tailed test is +1.96.The observed z value from sample data is -1.85.The decision made by the researcher based on this information is to _____ the null hypothesis.

The local swim team is considering offering a new semi-private class aimed at entry-level swimmers, but needs a minimum number of swimmers to sign up in order to be cost effective.Last year's data showed that during 8 swim sessions the average number of entry-level swimmers attending was 15.Suppose the instructor wants to conduct a hypothesis test and the alternative hypothesis is "the population mean is greater than 15." If the sample size is 5, $\sigma$ is known, and α = .01, the critical value of z is _______.

Business researchers sometimes need to test for equality of population variance.The hypothesis test about a population variance is performed using a chi-square test.

When a true null hypothesis is rejected, the researcher has made a Type I error.

A laptop battery lifespan follows a normal distribution with mean μ = 22 months and a standard deviation $\sigma$ = 6 months.To test the alternative hypothesis that μ < 22 with α = .01, 36 laptop batteries are randomly selected.Assuming that μ = 24, the probability of type II error is approximately ________.

Generally speaking, the hypotheses that business researchers want to prove are stated in the alternative hypothesis.

A "scientific hypothesis" _______________.

Suppose a researcher is testing a null hypothesis that $\mu$ = 61.A random sample of n = 36 is taken resulting in a sample mean of 63 and s = 9.The observed test statistic is _______.