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Chapter 10: Q. 29 (page 670)

According to sleep researchers, if you are between the ages of 12and 18years old, you need 9hours of sleep to be fully functional. A simple random sample of 28students 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 7.9hours, with a standard deviation of 2.1hours.

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

(a)t=7.9-92.128

(b)t=9-7.92.128

(c)t=7.9-92.128

(d)t=7.9-92.127

(e)t=9-7.92.127

Short Answer

Expert verified

The test statistic for the hypothesis test is (a)t=7.9-92.128

Step by step solution

01

Given information

We are given that if you are between the ages of 12and 18years old.The mean of the responses was 7.9hours, with a standard deviation of 2.1 hours. We have to find the test statistic for the hypothesis test

02

Simplify

As we know,

t=X-渭0sn

Where,

渭0=9(Hypothesized claim)

X=7.9(Sample mean )

n=28(Sample size)

s=2.1(Sample standard deviation)

By putting the values in above formula

t=7.9-92.128

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Most popular questions from this chapter

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.

Web business You want to compare the daily sales for two different designs of Web pages for your Internet business. You assign the next 60days to either Design A or Design B, 30days to each.

(a) Describe how you would assign the days for Design A and Design B using the partial line of random digits provided below. Then use your plan to select the first three days for using Design A. Show your method clearly on your paper.

24005521142622439078

(b) Would you use a one-sided or a two-sided significance test for this problem? Explain your choice. Then set up appropriate hypotheses.

(c) If you plan to use Table B to calculate the P-value, what are the degrees of freedom?

(d) The t statistic for comparing the mean sales is 2.06Using Table B, what P-value would you report? What would you conclude?

Men versus women The National Assessment of Educational Progress (NAEP) Young Adult Literacy Assessment Survey interviewed a random sample of 1917people 21to 25years old. The sample contained 840men and 1077women. 49The mean and standard deviation of scores on the NAEP's test of quantitative skills were x炉1=272.40and s1=59.2for the men in the sample. For the women, the results were x炉2=274.73and s2=57.5. Is the difference between the mean scores for men and women significant at the 1% level? Give appropriate statistical evidence to justify your answer.

鈥淲ould you marry a person from a lower social class than your own?鈥� Researchers asked this question of a random sample of 385black, never married students at two historically black colleges in the South. Of the 149men in the sample, 91said 鈥淵es.鈥� Among the 236women, 117said 鈥淵es.鈥�14Is there reason to think that different proportions of men and women in this student population would be willing to marry beneath their class?

Holly carried out the significance test shown below to answer this question. Unfortunately, she made some mistakes along the way. Identify as many mistakes as you can, and tell how to correct each one.

State: I want to perform a test of

H0:p1=p2

Ha:p1鈮�p2

at the 95%confidence level.

Plan: If conditions are met, I鈥檒l do a one-sample ztest for comparing two proportions.

  • Random The data came from a random sample of 385 black, never-married students.
  • Normal One student鈥檚 answer to the question should have no relationship to another student鈥檚 answer.
  • Independent The counts of successes and failures in the two groups鈥�91,58,117, and 119鈥�are all at least 10

Do: From the data, p^1=91149=0.61and p^2=117236=0.46.

Test statistic

z=(0.61-0.46)-00.61(0.39)149+0.46(0.54)236=2.91

p=value From Table A, role="math" localid="1650292307192" P(z鈮�2.91)鈮�1-0.3982鈮�0.0018.

Conclude: The p-value, 0.0018, is less than 0.05, so I鈥檒l reject the null hypothesis. This proves that a higher proportion of men than women are willing to marry someone from a social class lower than their own.

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鈥檚 manufacturer, when the large setting is chosen, the amount of liquid dispensed by the machine follows a Normal distribution with mean 27ounces and standard deviation0.8ounces. When the medium setting is chosen, the amount of liquid dispensed follows a Normal distribution with mean 17ounces and standard deviation 0.5ounces. To test the manufacturer鈥檚 claim, the restaurant manager measures the amount of liquid in a random sample of 25cups filled with the medium setting and a separate random sample of 20cups filled with the large setting. Let x炉1-x炉2be the difference in the sample mean amount of liquid under the two settings (large 鈥� medium). Find the mean and standard deviation of the sampling distribution.
See all solutions

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