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The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset Vaia Explanations$ Math

4th Edition · 809 pages

ISBN: 9781319113339

Chapter 10: Q. 2.1 (page 638)

The U.S. Department of Agriculture (USDA) conducted a survey to estimate the average price of wheat in July and in September of the same year. Independent random samples of wheat producers were selected for each of the two months. Here are summary statistics on the reported price of wheat from the selected producers, in dollars per bushel:
Construct and interpret a $99 %$ confidence interval for the difference in the mean wheat price in July and in September.

Short Answer

Expert verified

No, enough evidence are not provided by the data set that polyester decays more in $16$ weeks in comparison of $2$ weeks.

Step by step solution

01

Given information

02

Explanation

The null and alternative hypothesis is

$H_{0} : μ_{1} = μ_{2}$

$H_{a} : μ_{1} < μ_{2}$

The output came using $T i - 83$ plus calculator is

Assume, the significance level to be $0.05 %$

The null hypothesis is not rejected

At $5 %$ significance level, there are insufficient evidence to conclude that polyester decays more in $16$ weeks in comparison of $2$ weeks.

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Most popular questions from this chapter

Construct and interpret a $95 %$ confidence interval for $p_{1} - p_{2}$ in Exercise $23$ . Explain what additional information the confidence interval provides.

A fast-food restaurant uses an automated filling machine to pour its soft drinks. The machine has different settings for small, medium, and large drink cups. According to the machine’s manufacturer, when the large setting is chosen, the amount of liquid dispensed by the machine follows a Normal distribution with mean $27$ ounces and standard deviation $0.8$ ounces. When the medium setting is chosen, the amount of liquid dispensed follows a Normal distribution with mean $17$ ounces and standard deviation $0.5$ ounces. To test the manufacturer’s claim, the restaurant manager measures the amount of liquid in a random sample of $25$ cups filled with the medium setting and a separate random sample of $20$ cups filled with the large setting. Let $x_{1} - {\bar{x}}_{2}$ be the difference in the sample mean amount of liquid under the two settings (large – medium). Find the probability that ${\bar{x}}_{1} - {\bar{x}}_{2}$ is more than $12$ ounces. Show your work.

According to sleep researchers, if you are between the ages of $12$ and $18$ years old, you need $9$ hours of sleep to be fully functional. A simple random sample of $28$ students was chosen from a large high school, and these students were asked how much sleep they got the previous night. The mean of the responses was $7.9$ hours, with a standard deviation of $2.1$ hours.

Which of the following is the test statistic for the hypothesis test?

(a) $t = \frac{7.9 - 9}{\frac{2.1}{\sqrt{28}}}$

(b) $t = \frac{9 - 7.9}{\frac{2.1}{\sqrt{28}}}$

(c) $t = \frac{7.9 - 9}{\sqrt{\frac{2.1}{28}}}$

(d) $t = \frac{7.9 - 9}{\frac{2.1}{\sqrt{27}}}$

(e) $t = \frac{9 - 7.9}{\frac{2.1}{\sqrt{27}}}$

Credit cards and incentives A bank wants to know which of two incentive plans will most increase the use of its credit cards. It offers each incentive to a group of current credit card customers, determined at random, and compares the amount charged during the following six months.

(a) Is this a problem with comparing means or comparing proportions? Explain.

(b) What type of study design is being used to produce data?

A large toy company introduces a lot of new toys to its product line each year. The company wants to predict the demand as measured by y, first-year sales (in millions of dollars) using x, awareness of the product (as measured by the proportion of customers who had heard of the product by the end of the second month after its introduction). A random sample of $65$ new products was taken, and a correlation of $0.96$ was computed. Which of the following is a correct interpretation of this value?

(a) Ninety-six percent of the time, the least-squares regression line accurately predicts first-year sales.

(b) About $92 %$ of the time, the proportion of people who have heard of the product by the end of the second month will correctly predict first-year sales.

(c) About $92 %$ of first-year sales can be explained by the proportion of people who have heard of the product by the end of the second month.

(d) The least-squares regression line relating the proportion of people who have heard of the product by the end of the second month and first-year sales will have a slope of $0.96$ .

(e) Ninety-two percent of the variation in first-year sales can be explained by the least-squares regression line with proportion of people who have heard of the product by the end of the second month as the explanatory variable.

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