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Chapter 10: Q. 63 (page 658)

Looking back on love How do young adults look back on adolescent romance? investigators interviewed couples in their mid-twenties. The female and male partners were interviewed separately. Each was asked about his or her current relationship and also about a romantic relationship that lasted at least two months when they were aged 15or16 . One response variable was a measure on a numerical scale of how much the attractiveness of the adolescent partner mattered. You want to compare the men and women on this measure.

Short Answer

Expert verified

The appropriate procedure is Two sample t-test.

Step by step solution

01

Given Information

40 couples in their twenties were interviewed by experts. Separately, the female and male accomplices were met. Each was given information about their current relationship as well as a previous romantic relationship that lasted at least two months when they were 15or16 years old. One reaction variable was a numerical scale that indicated how much the young adult accomplice's attraction mattered. On this scale, you must examine both males and women.

02

Explanation

When the sample size is small, an independent two-sample test is used to see if the mean difference between two sets of observations is equal to, higher than, or lower than 0. Two separate groups of women and men were tested in this test method to see how they behaved.

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Most popular questions from this chapter

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鈥檛? Use information from the Minitab computer output below to support your answer.

Paired or unpaired? In each of the following settings, decide whether you should use paired t procedures or two-sample t procedures to perform inference. Explain your choice. 42

(a) To test the wear characteristics of two tire brands, A and B, each brand of tire is randomly assigned to 50 cards of the same make and model.

(b) To test the effect of background music on productivity, factory workers are observed. For one month, each subject works without music. For another month, the subject works while listening to music on an MP3 player. The month in which each subject listens to music is determined by a coin toss.

(c) A study was designed to compare the effectiveness of two weight-reducing diets. Fifty obese women who volunteered to participate were randomly assigned into two equal-sized groups. One group used Diet \(A\) and the other used Diet B. The weight of each woman was measured before the assigned diet and

39. Shoes How many pairs of shoes do teenagers have? To find out, a group of AP Statistics students conducted a survey. They selected a random sample of 20female students and a separate random sample of 20male students from their school. Then they recorded the number of pairs of shoes that each respondent reported having. The back-to-back stemplot below displays the data.

Based on your answer to Question 3, would you be surprised if the difference in the proportion of red crackers in the two samples was p1^-p^2=-0.02? Explain.

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.
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