Exam 9: Statistical Inference: Hypothesis Testing for Single Populations

Suppose you are testing the null hypothesis that a population mean is less than or equal to 46, against the alternative hypothesis that the population mean is greater than 46.If the sample size is 25, $\sigma$ is known, and α = .01, the critical value of z is _______.

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.Using $\alpha$ = 0.10, the critical "t" values are _______.

In many cases a business researcher gathers data to test a hypothesis about a single population mean and the value of the population standard deviation is unknown.In this case the researcher cannot use the z 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 38 defaulted loans.Using $\alpha$ = 0.10, the appropriate decision is to _______.

A small restaurant owner believes at least 36 % of his customers would be willing to order take out service if it were available.He is interested in surveying his customer base.He intends to use the following null and alternative hypotheses. H_o: p $\ge$ 0.36 H_a: p < 0.36 These hypotheses _______________.

Whenever hypotheses are established such that the alternative hypothesis is "μ > 8", where μ is the population mean, the p-value is the probability of observing a sample mean greater than the observed sample mean assuming that μ = 8.

A company has a contract to supply specialized batteries to a manufacturer with a mean width of 54mm and a variance of 1.8 or less with an alpha of 0.05.The company randomly tests 20 of these batteries to ensure that they are meeting the requirements of the contract.If the most recent test had a variance of 1.9, what would be the observed chi-squared value?

Power is equal to (1 - $\beta$ ), the probability of a test rejecting the null hypothesis that is indeed false.

The customer help center in your company receives calls from customers who need help with some of the customized software solutions your company provides.Your company claims that the average waiting time is 7 minutes at the busiest time, from 8 a.m.to 10 a.m., Monday through Thursday.One of your main clients has recently complained that every time she calls during the busy hours, the waiting time exceeds 7 minutes.You conduct a statistical study to determine the average waiting time with a sample of 35 calls for which you obtain an average waiting time of 8.15 minutes.If the population standard deviation is known to be 4.2 minutes, and α = 0.05, the appropriate decision is to ___________.

A statistically significant result is _______________.

The probability of committing a Type II error changes for each alternative value of the parameter.

Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of e-mail messages sent by GFS employees are not business related.A random sample of 300 e-mail messages was selected to test this hypothesis at the 0.01 level of significance.Fifty-four of the messages were not business related.The null hypothesis is ____.

A coffee-dispensing machine is supposed to deliver 8 ounces of liquid into each paper cup, but a consumer believes that the actual mean amount is less.The consumer obtained a sample of 16 cups of the dispensed liquid with sample mean of 7.75 ounces and sample variance of 0.81 ounces.If the dispensed liquid delivered per cup is normally distributed, the appropriate decision at α = 0.05 is to ___________.

Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of e-mail messages sent by GFS employees are not business related.A random sample of 300 e-mail messages was selected to test this hypothesis at the 0.01 level of significance.Sixty of the messages were not business related.The appropriate decision is to _______.

In testing hypotheses, the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it.

If car manufacturer of cars orders the windshields from another company.The width of the windshields received need to be within 0.2 mm of the average width.The contract between the car manufacturer and the windshield suppler should include a clause related to the delivered windshields' median.

Which of the following best describes a Type II error?

In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8, a random sample of 25 items is selected.The sample mean is 4.1 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 _______.

If a null hypothesis is not rejected at the 0.05 level of significance, the p-value is bigger than 0.05