StatisticsName ______

8.4-8.5ReviewDate _____

Directions: Use the following test statistic to test the claims.

You may use either the Traditional or P-Value Method.

  1. A machine fills bottles with fluid of liquid. The quality-control manager determines that the fill levels are normally distributed with a mean of and a standard deviation of . He has an engineer recalibrate the machine in an attempt to lower the standard deviation. After the recalibration, the quality-control manager randomly selects bottles from the line and determines that the standard deviation is

. The manager concludes that the standard deviation has decreased at the level of significance. Test his claim.

  1. Government regulations require that when a sunscreen is labeled “waterproof,” then it must still work after 80 minutes of immersion or carry claims of continuous protection after 6 to 8 hours in the water. To check on this claim, the consumer’s group randomly selects 20 samples and finds that they still work an average of 77 minutes after immersion with a standard deviation of 1.82 minutes. Assuming that the population is normally distributed, use a level of significance to determine if we should reject the manufacturer’s claim about “waterproof”?
  1. We often hear sports announcers say, “.” This is the announcer’s way of saying that the player is inconsistent – that his or her performance varies dramatically from game to game. Suppose the standard deviation of the number of points scored by shooting guards in the NBA is . A random sample of games played by Allen Iverson of the Philadelphia 76ers results in a sample standard deviation of points. Test the claim that Allen Iverson is more consistent than other shooting guards in the NBA at the level of significance.
  1. Government regulations require that when a sunscreen is labeled “waterproof,” then it must still work after 80 minutes of immersion or carry claims of continuous protection after 6 to 8 hours in the water. To check on this claim, the consumer’s group randomly selects 20 samples and finds that they still work an average of 77 minutes after immersion with a standard deviation of 1.82 minutes. Assuming that the population is normally distributed, use a level of significance to determine if we should reject the manufacturer’s claim about “waterproof”?
  1. Government regulations require that when a sunscreen is labeled “waterproof,” then it must still work after 80 minutes of immersion or carry claims of continuous protection after 6 to 8 hours in the water. To check on this claim, the consumer’s group randomly selects 20 samples and finds that they still work an average of 77 minutes after immersion with a standard deviation of 1.82 minutes. Assuming that the population is normally distributed, use a level of significance to determine if we should reject the manufacturer’s claim about “waterproof”?
  1. One measure of the risk of a mutual fund is the variance of its rate of return. Suppose a mutual fund qualifies as having moderate risk if the variance of its monthly rate of return is less than . A mutual-fund manager claims that his fund has moderate risk. A mutual-fund rating agency does not believe this claim and randomly selects months and determines the rate of return for the fund. The variance of the rate of return is compute to be . Test the mutual-fund manager’s claim at the level of significance.
  1. The claim is that for nicotine amounts in king-size cigarettes, The sample size is and the test statistics is . Find the or range of .
  1. A sociologist claims that the variance of ages at which women marry in Memphis, Tennessee, is greater than the variance age of years throughout the United States. Based upon a random sample of recently filed marriage certificates, she obtains the ages shown in the table below.Test her claim using the level of significance.

40 / 23 / 30 / 24 / 31
29 / 28 / 24 / 35 / 34
24 / 21 / 46 / 29 / 31
29 / 29 / 21 / 33 / 39