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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 16weeks in comparison of 2weeks.

Step by step solution

01

Given information

02

Explanation

The null and alternative hypothesis is

H0:μ1=μ2

Ha:μ1<μ2

The output came using Ti-83plus 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 16weeks in comparison of2weeks.

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Most popular questions from this chapter

44. Tropical flowers Different varieties of the tropical flower Heliconia are fertilized by different species of hummingbirds.

Researchers believe that over time, the lengths of the flowers and the forms of the hummingbirds’ beaks have evolved to match each other. Here are data on the lengths in millimeters for random samples of two color varieties of the same species of flower on the island of Dominica:

(a) A Fathom dotplot of the data is shown below. Use the graph to answer these questions:

  • Are the centers of the two groups similar or different? Explain
  • Are the spreads of the two groups similar or different? Explain.

(b) Construct and interpret a 95% confidence interval for the difference in the mean lengths of these two varieties of flowers.
(c) Does the interval support the researchers’ belief that the two flower varieties have different average lengths? Explain.

Do drivers reduce excessive speed when they encounter police radar? Researchers studied the behavior of a sample of drivers on a rural interstate highway in Maryland where the speed limit was 55miles per hour. They measured the speed with an electronic device hidden in the pavement and, to eliminate large trucks, considered only vehicles less than 20feet long. During some time periods (determined at random), police radar was set up at the measurement location. Here are some of the data.

Number of vehiclesNumber over65mphNo radar12,9315,690Radar3,2851,051

(a) The researchers chose a rural highway so that cars would be separated rather than in clusters because some cars might slow when they see other cars slowing. Explain why this is important.

(b) Does the proportion of speeding drivers differ significantly when the radar is being used and when it isn’t? Use information from the Minitab computer output below to support your answer.

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 65new products was taken, and a correlation of 0.96was 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.

A sample survey interviews SRSs of500female college students and 550male college students. Each student is asked whether he or she worked for pay last summer. In all, 410of the women and 484of the men say “Yes.” The 95%confidence interval for the difference pM-pFin the proportions of college men and women who worked last summer is about

(a) 0.06±0.00095

(b) 0.06±0.043.

(c) 0.06±0.036

(d) -0.06±0.043

(e)-0.06±0.036

45. Paying for college College financial aid offices expect students to use summer earnings to help pay for college. But how large are these earnings? One large university studied this question by asking a random sample of 1296students who had summer jobs how much they earned. The financial aid office separated the responses into two groups based on gender. Here are the data in summary form:

(a) How can you tell from the summary statistics that the distribution of earnings in each group is strongly skewed to the right? A graph of the data reveals no outliers. The use of two-sample t procedures is still justified. why?
(b) Construct and interpret a 90%confidence interval for the difference between the mean summer earnings of male and female students at this university.
(c) Interpret the 90%confidence level in the context of this study.
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