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Chapter 10: Q. 42 (page 666)

For their final project, a group of AP庐 Statistics students wanted to compare the texting habits of males and females. They asked a random sample of students from their school to record the number of text messages sent and received over a 2-day period. Here are their data:

Let 渭1=the true mean number of texts sent by male students at the school and 渭2=the true mean number of texts sent by female students at the school. Check if the conditions for calculating a confidence interval for 渭1-渭2 are met.

Short Answer

Expert verified

Females group text more than males.

Step by step solution

01

Step 1. Given information

Given:

02

Step 2. Calculation

Let鈥檚 take given table and find out its sum first:

X炉M=鈭�XMn=9367=133.71X炉F=鈭�XFn=20527=294.14

From the above ratio values of males and females, the mean value of female group is more than male group that鈥檚 why the female groups text more.

Hence, females group text more than males.

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Most popular questions from this chapter

A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with that in a school district of a large city. The researcher obtained an SRS of 60 high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be 6 hours with a standard deviation of 3 hours. The researcher also obtained an independent SRS of 40 high school students in a large city school district and found the mean time spent in extracurricular activities per week to be 5 hours with a standard deviation of 2 hours. Suppose that the researcher decides to carry out a significance test of H0:渭suburban=渭cityversus a two-sided alternative. Which is the correct standardized test statistic ?

(a)z=(6-5)-0360+240

(b) z=(6-5)-03260+2240

(c) role="math" localid="1654192807425" t=(6-5)-0360+240

(d) t=(6-5)-0360+240

(e)t=(6-5)-03260+2240

Are teenagers going deaf? In a study of 3000randomly selected teenagers in 1990,450showed some hearing loss. In a similar study of 1800 teenagers reported in 2010,351showed some hearing loss.

a. Do these data give convincing evidence that the proportion of all teens with hearing

loss has increased at the 伪=0.01 significance level?

b. Interpret the P-value from part (a) in the context of this study.

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.

According to sleep researchers, if you are between the ages of 12and 18years old, you need 9 hours of sleep to function well. 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 standardized test statistic for the hypothesis test ?

  1. localid="1654221307488" t=7.9-92.128andt=7.9-92.128
  2. t=9-7.92.128andt=9-7.92.128
  3. t=7.9-92.128and t=7.9-92.128
  4. localid="1654221494579" t=7.9-92.127andt=7.9-92.127
  5. localid="1654221497857" t=9-7.92.127andt=9-7.92.127

Researchers want to evaluate the effect of a natural product on reducing blood pressure. They plan to carry out a randomized experiment to compare the mean reduction in blood pressure of a treatment (natural product) group and a placebo group. Then they will use the data to perform a test of H0:渭T鈭�渭P=0versus Ha:渭T鈭�渭P>0, where 渭T= the true mean reduction in blood pressure when taking the natural product and 渭P = the true mean reduction in blood pressure when taking a placebo for subjects like the ones in the experiment. The researchers would like to detect whether the natural product reduces blood pressure by at least 7points more, on average, than the placebo. If groups of size 50are used in the experiment, a twosample t test using 伪=0.01will have a power of 80%to detect a 7-point difference in mean blood pressure reduction. If the researchers want to be able to detect a 5-point difference instead, then the power of the test

a. would be less than 80%.

b. would be greater than 80%.

c. would still be 80%.

d. could be either less than or greater than 80%.

e. would vary depending on the standard deviation of the data

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