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Chapter 10: Q.10 (page 664)

Students鈥� self-concept Here is SAS output for a study of the self-concept of a random sample of seventh-grade students. The variable SC is the score on the Piers-Harris Self-Concept Scale. The analysis was done to see if male and female students differ in mean self-concept score .

Write a few sentences summarizing the comparison of females and males, as if you were preparing a report for publication

Short Answer

Expert verified

There is not enough proof to reject the claim that the population mean is equal for men and women.

Step by step solution

01

Given Information

02

Explanation

The hypotheses:

H0:渭1=渭2

H1:渭1鈮�渭2

The test statistic:

t=x炉1-x炉2s12n1+s22n1

=55.516-57.91512.696231+12.265247

=-0.8276

03

Explanation

Degrees of freedom:

df=62.8

The P-value is the chance of having the test statistic's value, or a number that is more extreme.

P=0.4110

If the P-value is equal or les than to the significance level, then the null hypothesis is rejected:

P>0.05鈬�Fail to rejectH0

There is not enough proof to reject the claim that the population mean is equal for men and women.

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Most popular questions from this chapter

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.

The power takeoff driveline on tractors used in agriculture is a potentially serious hazard to operators of farm equipment. The driveline is covered by a shield in new tractors, but for a variety of reasons, the shield is often missing on older tractors. Two types of shields are the bolt-on and the flip-up. It was believed that the bolt-on shield was perceived as a nuisance by the operators and deliberately removed, but the flip-up shield is easily lifted for inspection and maintenance and may be left in place. In a study initiated by the U.S. National Safety Council, random samples of older tractors with both types of shields were taken to see what proportion of shields were removed. Of 183tractors designed to have bolt-on shields, 35 had been removed. Of the 136 tractors with flip-up shields, 15 were removed. We wish to perform a test of H0:pb-pif versus Ha:pb鈮�pf where pb and pf are the proportions of all tractors with the bolt-on and flip-up shields removed, respectively. Which of the following conditions for performing the appropriate significance test is definitely not satisfied in this case?

(a) Both populations are Normally distributed.

(b) The data come from two independent samples.

(c) Both samples were chosen at random.

(d) The counts of successes and failures are large enough to use Normal calculations.

(e) Both populations are at least 10 times the corresponding sample sizes

A surprising number of young adults (ages 19to 25) still live in their parents鈥� homes. A random sample by the National Institutes of Health included 2253men and 2629women in this age group. The survey found that 986of the men and 923of the women lived with their parents.

(a) Construct and interpret a 99%confidence interval for the difference in population proportions (men minus women).

(b) Does your interval from part (a) give convincing evidence of a difference between the population proportions? Explain.

To study the long-term effects of preschool programs for poor children, researchers designed an experiment. They recruited 123children who had never attended preschool from low-income families in Michigan. Researchers randomly assigned 62of the children to attend preschool (paid for by the study budget) and the other 61 to serve as a control group who would not go to preschool. One response variable of interest was the need for social services as adults. In the past 10years, 38children in the preschool group and 49in the control group have needed social services.

The Minitab output below gives a 95% con铿乨ence interval for p1-p2. Interpret this interval in context. Then explain what additional information the con铿乨ence interval provides.

48. Did the randomization produce similar groups? First, compare the two groups of birds in the first year. The only difference should be the
chance effect of the random assignment. The study report says: 鈥淚n the experimental year, the degree of synchronization did not differ between
food-supplemented and control females.鈥� For this comparison, the report gives t=-1.05.
(a) What type of tstatistic (one-sample, paired, or two-sample) is this? Justify your answer.
(b) Explain how this value of t leads to the quoted conclusion.

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