Exam 9: Introduction to Hypothesis Testing

The significance level in a hypothesis test corresponds to the maximum probability that a Type I error will be committed.

The produce manager for a large retail grocery store believes that an average head of lettuce weighs more than 1.7 pounds.If she were to test this statistically,what would the null and alternative hypotheses be and what is the research hypothesis?

A cell phone manufacturer claims that its phone will last for more than 8 hours of continuous talk time when the battery is fully charged.To test this claim a sample of n = 18 phones were tested.The results showed a sample mean of 8.2 hours and a sample standard deviation of 0.4 hours.Conduct the hypothesis test using a 0.5 level of significance and determine whether or not the company's claim is supported.

A major package delivery company claims that at least 95 percent of the packages it delivers reach the destination on time.As part of the evidence in a lawsuit against the package company,a random sample of n = 200 packages was selected.A total of 188 of these packages were delivered on time.Using a significance level of 0.05,the critical value for this hypothesis test is approximately 0.90.

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.Based on this,the null hypothesis should be rejected if > $1,854.66 approximately.

The manager of an online shop wants to determine whether the mean length of calling time of its customers is significantly more than 3 minutes.A random sample of 100 customers was taken.The average length of calling time in the sample was 3.1 minutes with a standard deviation of 0.5 minutes.At a 0.05 level of significance,it can be concluded that the mean of the population is

When deciding the null and alternative hypotheses,the rule of thumb is that if the claim contains the equality (e.g.,at least,at most,no different from,etc.),the claim becomes the null hypothesis.If the claim does not contain the equality (e.g.,less than,more than,different from),the claim is the alternative hypothesis.

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?

The loan manager for State Bank and Trust has claimed that the mean loan balance on outstanding loans at the bank is over $14,500.To test this at a significance level of 0.05,a random sample of n = 100 loan accounts is selected.Assuming that the population standard deviation is known to be $3,000,the value of that corresponds to the critical value is approximately $14,993.50.

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

One of the factors that a company will use in determining whether it will locate a new facility in a community is the status of the real estate market.The managers believe that an important measure of the real estate market is the average length of time that homes stay on the market before selling.They believe that if the mean time on the market is less than 45 days,the real estate market is favorable.To test this in a particular area,a random sample of n = 100 homes that sold during the past six months was selected.The mean for this sample was 40 days.It is believed that the population standard deviation is 15 days.If the test is conducted using a 0.05 level of significance,what conclusion should be reached?

Lube-Tech is a major chain whose primary business is performing lube and oil changes for passenger vehicles.The national operations manager has stated in an industry newsletter that the mean number of miles between oil changes for all passenger cars exceeds 4,200 miles.To test this,an industry group has selected a random sample of 100 vehicles that have come into a lube shop and determined the number of miles since the last oil change and lube.The sample mean was 4,278 and the standard deviation was known to be 780 miles.Based on this information,the p-value for the hypothesis test is less than 0.10.

Lube-Tech is a major chain whose primary business is performing lube and oil changes for passenger vehicles.The national operations manager has stated in an industry newsletter that the mean number of miles between oil changes for all passenger cars exceeds 4,200 miles.To test this,an industry group has selected a random sample of 100 vehicles that have come into a lube shop and determined the number of miles since the last oil change and lube.The sample mean was 4,278 and the standard deviation was known to be 780 miles.Based on a significance level of 0.10,the critical value for the test is approximately z = 1.28.

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 .

The cost of a college education has increased at a much faster rate than costs in general over the past twenty years.In order to compensate for this,many students work part- or full-time in addition to attending classes.At one university,it is believed that the average hours students work per week exceeds 20.To test this at a significance level of 0.05,a random sample of n = 20 students was selected and the following values were observed: Based on these sample data,the critical value expressed in hours:

Which of the following will be helpful if the decision maker wishes to reduce the chance of making a Type II error?

When the decision maker has control over the null and alternative hypotheses,the alternative hypotheses should be the "research" hypothesis.

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.

Woof Chow Dog Food Company believes that it has a market share of 25 percent.It surveys n = 100 dog owners and ask whether or not Woof Chow is their regular brand of dog food,and 23 people say yes.Based upon this information,what is the value of the test statistic?

A conclusion to "not reject" the null hypothesis is the same as the decision to "accept" the null hypothesis.