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Chapter 9: Q 44. (page 582)

Watching grass grow The germination rate of seeds is defined as the proportion of seeds that sprout and grow when properly planted and watered. A certain variety of grass seed usually has a germination rate of 0.80. A company wants to see if spraying the seeds with a chemical that is known to increase germination rates in other species will increase the germination rate of this variety of grass. The company researchers spray a random sample of 400grass seeds with the chemical, and 339of the seeds germinate. Do these data provide convincing evidence at the α=0.05 significance level that the chemical is

effective for this variety of grass?

Short Answer

Expert verified

The chemical are effective of grass of germination process.

Step by step solution

01

Given Information

It is given that n=400

x=339

p=0.05

02

Simplification

Null hypothesis is: H0:p=0.80

Alternate hypothesis: Ha:p≠0.80

Sample proportion is p^=xn

p^=339400=0.8475

Standard Deviation is: σp^=p(1-p)n

σp^=0.8(1-0.8)400=0.02

Zscore is Z=p^-pσp^

Z=0.8475-0.800.02=2.375

The probability value is P(x<Z)=0.99123

P(x>Z)=1-0.99123=0.0087745

P=0.0087745<0.05, null hypothesis is rejected.H0:p=0.80

Chemical is effective for variety of grass.

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Most popular questions from this chapter

Teen drivers Refer to Exercise 51.

a. Construct and interpret a 95% confidence interval for the true proportion p of all teens in the state who passed their driving test on the first attempt. Assume that the conditions for inference are met.

b. Explain why the interval in part (a) provides more information than the test in Exercise 51.

Jump around Student researchers Haley, Jeff, and Nathan saw an article on the Internet claiming that the average vertical jump for teens was 15 inches. They wondered if the average vertical jump of students at their school differed from 15 inches, so they obtained a list of student names and selected a random sample of 20 students. After contacting these students several times, they finally convinced them to allow their vertical jumps to be measured. Here are the data (in inches):

Do these data provide convincing evidence at the α=0.10 level that the average vertical jump of students at this school differs from 15 inches?

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a. State an appropriate pair of hypotheses for a significance test in this setting. Be sure to define the parameter of interest.

b. Check conditions for performing the test in part (a).

c. The 90% confidence interval for the mean daily water intake is 30.35 to 36.92 ounces. Based on this interval, what conclusion would you make for a test of the hypotheses in part (a) at the 10% significance level?

d. Do we have convincing evidence that the amount of water U.S. children drink per day differs from 40 ounces? Justify your answer.

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