Exam 9: Statistical Inference: Hypothesis Testing for Single Populations

The p-value 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 critical values of chi-square are ________.

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 _______.

A z test of proportions is used when a hypothesis test is conducted on a population proportion.

In conducting the z test of proportions, the sample proportion is computed by dividing the number of items being counted by the estimated total population.

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 observed value of chi-square is _________________.

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 and the level of significance is 0.05.The critical value found in the "t" table for this problem is _______.

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

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.What would be the null hypothesis each time the company conducts the test of the variances?

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 should the company do?

The customer help center in your company receives calls from customers who need help with some of the customized software solutions your company provides.Previous studies had indicated that 20% of customers who call the help center are Hispanics whose native language is Spanish and therefore would prefer to talk to a Spanish-speaking representative.This figure coincides with the national proportion, as shown by multiple larger polls.You want to test the hypothesis that 20% of the callers would prefer to talk to a Spanish-speaking representative.You conduct a statistical study with a sample of 35 calls and find out that 11 of the callers would prefer a Spanish-speaking representative.The significance level for this test is 0.01.The value of the test statistic obtained is:

Hypotheses are tentative explanations of a principle operating in nature.

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 ________.

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 critical value of this chi-squared 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 to __________.

A company believes that it controls more than 30% of the total market share for one of its products.To prove this belief, a random sample of 144 purchases of this product is contacted.It is found that 50 of the 144 purchases were of this company's brand.If a researcher wants to conduct a statistical test for this problem, the observed z value would be _______.

A laptop battery lifespan follows a normal distribution with mean μ = 20 months and a standard deviation $\sigma$ = 6 months.To test the alternative hypothesis that μ > 20 with α = .05, 36 laptop batteries are randomly selected.Assuming that μ = 21, the power of this is approximately ________.

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 should the company do?

Suppose that H_o: $\mu$$\le$ 0.01 H_a: $\mu$ > 0.01 The value 0.01 is the maximum safe level of some naturally occurring lethal pollutant in drinking water for human consumption.You need to decide if you will use water coming from a specific source for one of the beverages your company produces, based on sample measures of this pollutant taken in random different locations and times at the source of water.In this case you would want to

Albert Miller, VP of Production of a company that produces components for auto braking systems is examining the diameter of a specialized electrical wire produced with newly acquired machines in a new production line.For safety reasons, it is important that the variance in the diameter doesn't exceed 0.15 inches.Albert knows that the variance of the other production lines is 0.15 and he wants to make sure the new machine also delivers products whose variance doesn't exceed the safety limit.His staff randomly selects a sample of 25 wires and find out that the standard deviation of the sample is 0.42 inches.Assume that wire diameters are normally distributed.Using $\alpha$ = 0.10, the appropriate decision is ________.