Exam 9: Introduction to Hypothesis Testing

The director of the city Park and Recreation Department claims that the mean distance people travel to the city's greenbelt is more than 5.0 miles. Assume that the population standard deviation is known to be 1.2 miles and the significance level to be used to test the hypothesis is 0.05 when a sample size of n = 64 people are surveyed. Given this information, if the sample mean is 15.90 miles, the null hypothesis should be rejected.

When using the p-value method for a two-tailed hypothesis, the p-value is found by finding the area in the tail beyond the test statistic, then doubling it.

A small city is considering breaking away from the county school system and starting its own city school system. City leaders believe that more than 60 percent of residents support the idea. A poll of n = 215 residents is taken and 134 people say they support starting a city school district. Using a 0.10 level of significance, conduct a hypothesis test to determine whether this poll supports the belief of city leaders.

A major airline has stated in an industry report that its mean onground time between domestic flights is less than 18 minutes. To test this, the company plans to sample 36 randomly selected flights and use a significance level of .10. Assuming that the population standard deviation is known to be 4.0 minutes, if the true population mean is 16 minutes, the decision maker could end up making either a Type I or a Type II error depending on the sample result.

For the following hypothesis:

Hypothesis testing and confidence interval estimation are essentially two totally different statistical procedures and share little in common with each other.

You are given the following null and alternative hypotheses: If the true population mean is 4,345, calculate the power of the test. Assume the population standard deviation is known to be 200 and the sample size is 100.

For the following hypothesis test: With n= 0.42 and p = 0.42, state the conclusion

In a one-tailed hypothesis test, the larger the significance level, the greater the critical value will be.

The director of the city Park and Recreation Department claims that the mean distance people travel to the city's greenbelt is more than 5.0 miles. Assuming that the population standard deviation is known to be 1.2 miles and the significance level to be used to test the hypothesis is 0.05 when a sample size of n = 64 people are surveyed, the critical value is approximately 4.75 miles.

The state insurance commissioner believes that the mean automobile insurance claim filed in her state exceeds $1,700. To test this claim, the agency has selected a random sample of 20 claims and found a sample mean equal to $1,733 and a sample standard deviation equal to $400. They plan to conduct the test using a 0.05 significance level. Given this, the appropriate null and alternative hypotheses are H0 : ≤ $1,700 HA : > $1,700

For a given sample size n, if the level of significance (α) is decreased, the power of the test:

For the following hypothesis test: With n = 64 and p = 0.42, state the calculated value of the test statistic

A contract with a parts supplier calls for no more than .04 defects in the large shipment of parts. To test whether the shipment meets the contract, the receiving company has selected a random sample of n = 100 parts and found 6 defects. If the hypothesis test is to be conducted using a significance level equal to 0.05, what is the test statistic and what conclusion should the company reach based on the sample data?

When using the t-distribution in a hypothesis test, the population does not need to be assumed normally distributed.

A city newspaper has stated that the average time required to sell a used car advertised in the paper is less than 5 days. Assuming that the population standard deviation is 2.1 days, if the "true" population mean is 4.1 days and a sample size of n = 49 is used with an alpha equal to 0.05, the probability that the hypothesis test will lead to a Type II error is approximately .0869.

Waiters at Finegold's Restaurant and Lounge earn most of their income from tips. Each waiter is required to "tip-out" a portion of tips to the table bussers and hostesses. The manager has based the "tip- out" rate on the assumption that the mean tip is at least 15% of the customer bill. To make sure that this is the correct assumption, he has decided to conduct a test by randomly sampling 60 bills and recording the actual tips. State the appropriate null and alternative hypotheses.

For the following hypothesis:

A report recently published in a major business periodical stated that the average salary for female managers is less than $50,000. If we were interested in testing this, the following null and alternative hypotheses would be established: H0 : μ ≥ 50,000 Hα : μ < 50,000

If a real estate market is strong there will be a close relationship between the asking price for homes and the selling price. Suppose that one analyst believes that the mean difference between asking price and selling price for homes in a particular market area is less than $2,000. To test this using an alpha level equal to 0.05, a random sample of n = 15 homes that have sold recently was selected. The sample differences between asking price and selling price are in the following table: Based on these sample data, what is the critical value expressed in dollars?