Exam 9: Statistical Inference: Hypothesis Testing for Single Populations

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 _______.

In testing a hypothesis about a population variance,the chi-square test is fairly robust to the assumption the population is normally distributed.

If a null hypothesis was rejected at the 0.025 level of significance,it will be rejected at a 0.01 level of significance based on the same sample results.

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

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 _______.

When a false null hypothesis is rejected,the researcher has made a Type II error.

Discrete Components,Inc.manufactures a line of electrical resistors.Presently,the carbon composition line is producing 100 ohm resistors.The population variance of these resistors "must not exceed 4" to conform to industry standards.Periodically,the quality control inspectors check for conformity by randomly select 10 resistors from the line,and calculating the sample variance.The last sample had a variance of 4.36.Assume that the population is normally distributed.Using $\alpha$ = 0.05,the critical value of chi-square is _________________.

In performing a hypothesis test where the null hypothesis is that the population mean is 23 against the alternative hypothesis that the population mean is not equal to 23,a random sample of 17 items is selected.The sample mean is 24.6 and the sample standard deviation is 3.3.It can be assumed that the population is normally distributed.The degrees of freedom associated with this are _______.

When conducting a hypothesis test is on a population proportion the value of q is defined as p + 1.

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 null hypothesis is __________.

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

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.Using $\alpha$ = 0.10,the critical z value is _______.

Discrete Components,Inc.manufactures a line of electrical resistors.Presently,the carbon composition line is producing 100 ohm resistors.The population variance of these resistors "must not exceed 4" to conform to industry standards.Periodically,the quality control inspectors check for conformity by randomly selecting 10 resistors from the line,and calculating the sample variance.The last sample had a variance of 4.36.Assume that the population is normally distributed.Using $\alpha$ = 0.05,the null hypothesis is _________________.

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

The probability of committing a Type I error is called the power of the test.

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 level of significance is selected to be 0.10.The table "t" value for this problem is _______.

The rejection and nonrejection regions are divided by a point called the critical value.

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.Using $\alpha$ = 0.10,the observed z value is _______.

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 _______.

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 ____.