Exam 9: Introduction to Hypothesis Testing

A company that makes shampoo wants to test whether the average amount of shampoo per bottle is 16 ounces. The standard deviation is known to be 0.20 ounces. Assuming that the hypothesis test is to be performed using 0.10 level of significance and a random sample of n = 64 bottles, how large could the sample mean be before they would reject the null 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 hour. Conduct the hypothesis test using a 0.5 level of significance and determine whether or not the company's claim is supported.

When testing a hypothesis involving population proportions, an increase in sample size will result in a smaller chance of making a Type I statistical error.

Hono Golf is a manufacturer of golf products in Taiwan and China. One of the golf accessories it produces at its plant in Tainan Hsing, Taiwan, is plastic golf tees. The injector molder produces golf tees that are designed to have an average height of 66 mm. To determine if this specification is met, random samples are taken from the production floor. One sample is contained in the file labeled THeight. If the hypothesis test determines the specification is not being met, the production process will be shut down while causes and remedies are determined. At times this occurs even though the process is functioning to specification. What type of statistical error would this be?

In conducting a hypothesis test where the conclusion is to reject the null hypothesis, then either a correct decision has been made or else a Type I error.

At a recent meeting, the manager of a national call center for a major Internet bank made the statement that the average past-due amount for customers who have been called previously about their bills is now no larger than $20.00. Other bank managers at the meeting suggested that this statement may be in error and that it might be worthwhile to conduct a test to see if there is statistical support for the call center manager's statement. The file called Bank Call Center contains data for a random sample of 67 customers from the call center population. Assuming that the population standard deviation for past due amounts is known to be $60.00, what should be concluded based on the sample data? Test using α = 0.10.

What is meant by the terms Type I and Type II statistical error?

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:

Whenever possible, in establishing the null and alternative hypotheses, the research hypothesis should be made the alternative hypothesis.

Of the two types of statistical errors, the one that decision makers have most control over is Type I error.

In a two-tailed hypothesis test the area of both tails in the rejection region is equal to α.

If a decision maker is concerned that the chance of making a Type II error is too large, one option that will help reduce the risk is to reduce the significance level.

If the sample data lead the decision maker to reject the null hypothesis, the alpha level is the maximum probability of committing a Type II error.

For the following hypothesis test:

An issue that faces individuals investing for retirement is allocating assets among different investment choices. Suppose a study conducted 10 years ago showed that 65% of investors preferred stocks to real estate as an investment. In a recent random sample of 900 investors, 540 preferred real estate to stocks. Is this new data sufficient to allow you to conclude that the proportion of investors preferring stocks to real estate has declined from 10 years ago? Conduct your analysis at the α = 0.02 level of significance.

A consumer group plans to test whether a new passenger car that is advertised to have a mean highway miles per gallon of at least 33 actually meets this level. They plan to test the hypothesis using a significance level of 0.05 and a sample size of n = 100 cars. It is believed that the population standard deviation is 3 mpg. Based upon this information, if the "true" population mean is 32.0 mpg, what is the probability that the test will lead the consumer group to reject the claimed mileage for this car?

Type II errors are typically greater for two-tailed hypothesis tests than for one-tailed tests.

For the following z-test statistic, compute the p-value assuming that the hypothesis test is a one- tailed test: z = -1.55.

A company makes a device that can be fitted to automobile engines to improve the mileage. The company claims that if the device is installed, owners will observe a mean increase of more than 3.0 mpg. Assuming that the population standard deviation of increase is known to be 0.75 mpg, and a sample of size 64 cars is selected with an = 3.25 mpg, use the p-value approach to test the null hypothesis using a significance level of 0.05.

For the following hypothesis test: