Exam 9: Statistical Inference: Hypothesis Testing for Single Populations

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.

When using the t test to test a hypothesis about a population mean with an unknown population standard deviation ( $\sigma$ )the degrees of freedom is defined as n-1.

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.

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.Ninety employees rate the management as participatory.The appropriate decision is __________.

A researcher is testing a hypothesis of a single mean.The critical z value for $\alpha$ = .05 and an one?tailed test is 1.645.The observed z value from sample data is 1.13.The decision made by the researcher based on this information is to ______ the null hypothesis.

Jennifer Cantu,VP of Customer Services at Tri-State Auto Insurance,Inc.,monitors the claims processing time of the claims division.Her standard includes "a mean processing time of 5 days or less." Each week,her staff checks for compliance by analyzing a random sample of 60 claims.Jennifer's null hypothesis is ________.

Increasing the sample size reduces the probability of committing a Type I and Type II simultaneously.

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

When the population standard deviation ( $\sigma$ )is unknown,the value of s-1 is used to compute the t value.

A political scientist wants to prove that a candidate is currently carrying more than 60% of the vote in the state.She has her assistants randomly sample 200 eligible voters in the state by telephone and only 90 declare that they support her candidate.The observed z value for this problem is _______.

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 _______.

.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 alpha = .01,the critical value of z is _______.

A researcher is testing a hypothesis of a single mean.The critical z value for $\alpha$ = .05 and a two?tailed test is +1.96.The observed z value from sample data is -2.11.The decision made by the researcher based on this information is to _____ the null 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 t value is _______.

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 appropriate decision is _______.

The value of committing a Type II error is defined by the researcher prior to the study.

If a null hypothesis was not rejected at the 0.10 level of significance,it will be rejected at a 0.05 level of significance based on the same sample results.

A home building company routinely orders standard interior doors with a height of 80 inches.Recently the installers have complained that the doors are not the standard height.The quality control inspector for the home building company is concerned that the manufacturer is supplying doors that are not 80 inches in height.In an effort to test this,the inspector is going to gather a sample of the recently received doors and measure the height.The alternative hypothesis for the statistical test to determine if the doors are not 80 inches is

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 = .05,36 laptop batteries are randomly selected.Assuming that μ=21,the probability of type II error is approximately

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 _______.