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Chapter 10: q.86 (page 688)

Does drying barley seeds in a kiln increase the yield of barley? A famous

experiment by William S. Gosset (who discovered the t distributions) investigated this

question. Eleven pairs of adjacent plots were marked out in a large field. For each pair,

regular barley seeds were planted in one plot and kiln-dried seeds were planted in the

other. A coin flip was used to determine which plot in each pair got the regular barley seed

and which got the kiln-dried seed. The following table displays the data on barley yield

(pound per acre) for each plot.

Do these data provide convincing evidence at the α=0.05 level

that drying barley seeds in a kiln increases the yield of barley, on average?

Short Answer

Expert verified

The actual mean difference (regular–kiln dried) in yield between regular barley seeds and kiln-dried seeds is less than 0.

Step by step solution

01

given information

sample size = 10.

significance level = 0.05

02

we have to find that drying barley seeds in a kiln increases the yield of barley, on average

Hypotheses

The actual mean difference in yield between regular barley seeds and kiln-dried seeds is 0.

The actual mean difference in yield between regular barley seeds and kiln-dried seeds is less than 0.

03

samples are taken as random

Normal: n = 50 > 30.

The number of employees in this company is > 10 (50) = 500.

Calculations

Perform a t-test

df = 50 – 1 = 49 P-value = 0.01856

p (0.019 0.05), so we reject h0.

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Most popular questions from this chapter

Better barley Does drying barley seeds in a kiln increase the yield of barley? A famous experiment by William S. Gosset (who discovered the t distributions) investigated this question. Eleven pairs of adjacent plots were marked out in a large field. For each pair, regular barley seeds were planted in one plot and kiln-dried seeds were planted in the other. A coin flip was used to determine which plot in each pair got the regular barley seed and which got the kiln-dried seed. The following table displays the data on barley yield (pound per acre) for each plot.

Do these data provide convincing evidence at the α=0.05level that drying barley seeds in a kiln increases the yield of barley, on average?

Children make choices Many new products introduced into the market are

targeted toward children. The choice behavior of children with regard to new products is of particular interest to companies that design marketing strategies for these products. As part of one study, randomly selected children in different age groups were compared on their ability to sort new products into the correct product category (milk or juice). Here are some of the data:

Researchers want to know if a greater proportion of 6- to 7-year-olds can sort correctly than 4- to5-year-olds.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

b. Check if the conditions for performing the test are met.

Friday the 13th Do people behave differently on Friday the13th? Researchers collected data on the number of shoppers at a random sample of 45grocery stores on Friday the 6thand Friday the 13thin the same month. Then they calculated the difference (subtracting in the order6thminus13th ) in the number of shoppers at each store on these 2days. The mean difference is -46.5and the standard deviation of the differences is 178.0.

a. If the result of this study is statistically significant, can you conclude that the difference in shopping behavior is due to the effect of Friday the 13thon people’s behavior? Why or why not?

b. Do these data provide convincing evidence at theα=0.05level that the number of shoppers at grocery stores on these 2days differs, on average?

c. Based on your conclusion in part (a), which type of error—a Type I error or a Type II error—could you have made? Explain your answer.

A random sample of 100of last year’s model of a certain popular car found that 20had a specific minor defect in the brakes. The automaker adjusted the production process to try to reduce the proportion of cars with the brake problem. A random sample of 350of this year’s model found that 50had the minor brake defect.

a. Was the company’s adjustment successful? Carry out an appropriate test to support your answer. b. Based on your conclusion in part (a), which mistake—a Type I error or a Type II error—could have been made? Describe a possible consequence of this error.

A 96% confidence interval for the proportion of the labor force that is unemployed in a certain city is (0.07,0.10). Which of the following statements is true?

a. The probability is 0.96 that between 7%and10% of the labor force is unemployed.

b. About 96% of the intervals constructed by this method will contain the true proportion of the labor force that is unemployed in the city.

c. In repeated samples of the same size, there is a 96% chance that the sample proportion will fall between 0.07and0.10.

d. The true rate of unemployment in the labor force lies within this interval 96% of the time.

e. Between 7%and10%of the labor force is unemployed 96% of the time.
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