Chapter 10 AP Statistics

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ASSUME THE GIVEN DISTRIBUTION IS NORMAL.

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The manufacturer of a particular brand of microwave popcorn claims that only 2 percent of its kernels of corn fail to pop. A competitor, believing that the actual percentage is larger, tests 2,000 kernels and finds that 44 failed to pop. Do these results provide sufficient evidence to support the competitor's belief?

• One-Sample Z Test for a Proportion

• One-Sample T Test for a Mean

• Two-Sample Z Test for a Proportion

• Matched-Pairs T Test for a Mean

White blood cell counts are normally distributed with mean 7500 and variance 500. If a patient has taken 50 laboratory blood tests that have a mean of 6899.75 and a standard deviation of 393.44, does this give evidence that his white blood cell count is significantly different than normal?

• One-Sample T Test for a Mean

• One-Sample Z Test for a Proportion

• One-Sample Z Test for a Mean

• One-Sample T Test for a Proportion

USA Today reported that in 1992, 39% of all elementary school children claimed that when they grow up they want to do something to help other people. However, in 1995, 128 of a random sample of 317 of these same children claimed that when they grow up they want to do something to help other people. Does this information indicate that there has been an attitude change either way?

• One-Sample Z Test for a Proportion

• Two-Sample Z Test for the Difference in Proportions

• One-Sample T Test for a Mean

• Two-Sample T Test for the Difference in Means

The manager of a sporting goods store offered a bonus commission to his salespeople when they sold more goods. A new manager dropped the bonus system. For a random sample of six sales people, the weekly sales (in thousands of dollars) are shown in the following table with and without the bonus system
Salesperson   1 2 3 4 5 6
with bonus 2.9 3.0 5.8 4.4 5.3 5.6
w/o bonus 2.8 2.5 5.9 3.5 4.6 4.6
difference 0.1 0.5 -0.1 0.9 0.7 1.0

• Matched-Pairs T Test for a Mean

• One-Sample T Test for a Mean

• Two-Sample T Test for the Difference in Means

The following is based on information taken from Winter Wind Studies in Rocky Mountain National Park, by Glidden. At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (mi/hr) in January and April are recorded below:
Weather station 1 2 3 4 5
January 139 122 126 64 78
April 104 113 100 88 61
Difference 35 9 26 -24 17
Does this information indicate that the peak wind gusts are higher in January than April?

• Two-Sample T Test for the Difference in

• Matched-Pairs T Test for a Mean

• One-Sample T Test for a Mean

In 1975, a random sample of 1484 adult U.S. citizens was surveyed, and 193 strongly agreed with the statement, "People should take care of themselves". Then, in 1991, a survey of 1013 adult U.S. citizens showed that only 61 strongly agreed with the statement. Does this indicate that the proportion of U.S.adults who strongly agree with the given statement has dropped?

• Two-Sample Z Test for the Difference in Proportions

• Two-Sample T Test for the Difference in Means

• Matched Pairs T Test for a Mean

• One-Sample T Test for a Mean

Dannon is supposed to put 29.6 grams of fruit in their fruit-flavored yogurt. To see if enough fruit is being placed in cups of fruit-flavored yogurt, a quality inspector measured the amount in 27 containers.She found an average of 28.9 grams of fruit and standard deviation of 2.8 grams. Does this show that there is probably enough yogurt in the cups?

• One-Sample T Test for a Mean

• One-Sample Z Test for a Proportion

• Matched-Pairs T Test for a Mean

• Chi-Square Goodness of Fit Test

A leading auto manufacturer claimed that a popular version of its minivan was available in the Midwest foran average price or $16,000 with a standard deviation of $800. A consumer group doubted that report andsurveyed 50 recent purchasers of the minivan to dispute the manufacturer's claim. They came up with anaverage of $16,277. Does this show that the manufacturer is making a false claim?

• One-Sample Z Test for a Mean

• Matched-Pairs T Test for a Mean

• Two-Sample T Test for the Difference in Means

• One-Sample Z Test for a Proportion