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Chapter 10: Q. 99 (page 691)

Which inference method?

a. Drowning in bathtubs is a major cause of death in children less than5years old. A random sample of parents was asked many questions related to bathtub safety. Overall,85%of the sample said they used baby bathtubs for infants. Estimate the percent of all parents of young children who use baby bathtubs.

b. How seriously do people view speeding in comparison with other annoying behaviors? A large random sample of adults was asked to rate a number of behaviors on a scale of1(no problem at all) to5(very severe problem). Do speeding drivers get a higher average rating than noisy neighbors?

c. You have data from interviews with a random sample of students who failed to graduate from a particular college in7years and also from a random sample of students who entered at the same time and did graduate within7years. You will use these data to estimate the difference in the percent's of students from rural backgrounds among dropouts and graduates.

d. Do experienced computer-game players earn higher scores when they play with someone present to cheer them on or when they play alone? Fifty teenagers with experience playing a particular computer game have volunteered for a study. We randomly assign25 of them to play the game alone and the other25to play the game with a supporter present. Each player鈥檚 score is recorded.

Short Answer

Expert verified

(a) The inference method is a one-sample z interval for proportion.

(b) The inference method is a one-sample t-interval for the mean.

(c) The inference method is a one-sample z interval for proportion.

(d) The inference method is a one-sample z interval for proportion.

Step by step solution

01

Part (a) Step 1: Given Information

We are given that drowning in bath tubs is major cause of death of children and we have to find out the inference method.

02

Part (a) Step 2: Explanation

According to the question, when we use null hypothesis or confidence interval for proportion, we use z-test or z-interval and it is given in the sample that the proportion of infants death in drawing bathtubs and for that use z-interval.

Hence, z-interval is used.

03

Part (b) Step 1: Given Information

We are given that people view speeding in comparison with other annoying behaviors, and we have to find out the inference method.

04

Part (b) Step 2: Explanation

According to the question, when we use null hypothesis or confidence interval for mean, we use t-test or t-interval, and it is given in the sample that the two subjects are taken and they are the same and dependent on each other, and use paired test or paired interval.

Hence, t-interval is used.

05

Part (c) Step 1: Given Information

We are given data from interviews with a random sample of students who failed to graduate from a particular college and we have to find out the inference method.

06

Part (c) Step 2: Explanation

According to the question, when we use null hypothesis or confidence interval for proportions, we use z-test or z-interval, and it is given in the sample that the two subjects are taken and they are different and independent of each other, and use sample test or sample interval.

Hence, z-interval is used.

07

Part (d) Step 1: Given Information

We are given computer game-player experience to earn higher scores when they play with someone present to cheer them on or when they play alone, and we have to find out the inference method.

08

Part (d) Step 2: Explanation

According to the question, when we use null hypothesis or confidence interval for proportions, we use z-test or z-interval, and it is given in the sample that the two subjects are taken and they are different and independent of each other, and use sample test or sample interval.

Hence, z-interval is used.

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Most popular questions from this chapter

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 boll-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 US 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, 35had been removed. Of the 156tractors with flip-up shields, 15were removed. We wish to perform a test of H0:pb=pfversus Ha:pb>pf, where pband pfare the proportions of all the tractors with bolt-on and flip-up shields removed, respectively. Which of the following is not a condition for performing the significance test ?

(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 10times the corresponding sample sizes.

An agricultural station is testing the yields for six different varieties of seed corn. The station has four large fields available, located in four distinctly different parts of the county. The agricultural researchers consider the climatic and soil conditions in the four parts of the county as being quite different, but are reasonably confident that the conditions within each field are fairly similar throughout. The researchers divide each field into six sections and then randomly assign one variety of corn seed to each section in that field. This procedure is done for each field. At the end of the growing season, the corn will be harvested, and the yield (measured in tons per acre) will be compared. Which one of the following statements about the design is correct?

a. This is an observational study because the researchers are watching the corn grow.

b. This a randomized block design with fields as blocks and seed types as treatments.

c. This is a randomized block design with seed types as blocks and fields as treatments.

d. This is a completely randomized design because the six seed types were randomly assigned to the four fields.

e. This is a completely randomized design with24迟谤别补迟尘别苍迟蝉鈥�6 seed types and 4 fields.

Music and memory Does listening to music while studying help or hinder students鈥� learning? Two statistics students designed an experiment to find out. They selected a random sample of 30students from their medium-sized high school to participate. Each subject was given 10minutes to memorize two different lists of 20words, once while listening to music and once in silence. The order of the two word lists was determined at random; so was the order of the treatments. The difference (Silence 鈭� Music) in the number of words recalled was recorded for each subject. The mean difference was 1.57and the standard deviation of the differences was 2.70.

a. If the result of this study is statistically significant, can you conclude that the difference in the ability to memorize words was caused by whether students were performing the task in silence or with music playing? Why or why not?

b. Do the data provide convincing evidence at the伪=0.01 significance level that the number of words recalled in silence or when listening to music differs, on average, for students at this school?

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

Young adults living at home A surprising number of young adults (ages 19

to 25) still live in their parents鈥� homes. The National Institutes of Health surveyed

independent random samples of 2253men and 2629women in this age group. The survey found that 986 of the men and 923 of the women lived with their parents.

a. Construct and interpret a 99%confidence interval for the difference in the true

proportions of men and women aged 19-25who live in their parents鈥� homes.

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

Children make choices Refer to Exercise 15.

a. Explain why the sample results give some evidence for the alternative hypothesis.

b. Calculate the standardized test statistic and P-value.

c. What conclusion would you make?
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