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Reading level A school librarian purchases a novel for her library. The publisher claims that the book is written at a fifth-grade reading level, but the librarian suspects that the reading level is lower than that. The librarian selects a random sample of $40$pages and uses a standard readability test to assess the reading level of each page. The mean reading level of these pages is $4.8$ with a standard deviation of $0.8.$Do these data give convincing

evidence at the $\mathrm{Î\pm }=0.05$significance level that the average reading level of this novel is less than 5?

How much juice? One company’s bottles of grapefruit juice are filled by a machine that is set to dispense an average of 180 milliliters (ml) of liquid. The company has been getting negative feedback from customers about underfilled bottles. To investigate, a quality-control inspector takes a random sample of 40 bottles and measures the volume of liquid in each bottle. The mean amount of liquid in the bottles is 179.6 ml and the standard deviation is 1.3 ml. Do these data provide convincing evidence at the$\mathrm{Î\pm }=0.05$significance level that the machine is underfilling the bottles?

Pressing pills A drug manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The hardness of a sample from each batch of tablets produced is measured to control the compression process. The target value for the hardness is $\mathrm{μ}=11.5$The hardness data for a random sample of 20 tablets from one large batch are

Is there convincing evidence at the $5\%$level that the mean hardness of the tablets in this batch differs from the target value?

Jump around Student researchers Haley, Jeff, and Nathan saw an article on the Internet claiming that the average vertical jump for teens was $15$ inches. They wondered if the average vertical jump of students at their school differed from $15$ inches, so they obtained a list of student names and selected a random sample of $20$ students. After contacting these students several times, they finally convinced them to allow their vertical jumps to be measured. Here are the data (in inches):

Do these data provide convincing evidence at the $\mathrm{Î\pm }=0.10$ level that the average vertical jump of students at this school differs from 15 inches?

Pressing pills Refer to Exercise 77.

a. Construct and interpret a 95% confidence interval for the true hardness μ of the tablets in this batch. Assume that the conditions for inference are met.

b. Explain why the interval in part (a) is consistent with the result of the test in Exercise 77.

Stating hypotheses

a. A change is made that should improve student satisfaction with the parking situation at your school. Before the change, $37\%$of students approve of the parking that's provided. The null hypothesis $\mathrm{H}0:{\mathrm{p}}^{âˆ\S =0.37}{H}_0:\hat{p}=0.37$is tested against the alternative Ha: ${\mathrm{p}}^{âˆ\S >0.37}{H}_a:\hat{p}>0.37$

b. A researcher suspects that the mean birth weights of babies whose mothers did not see a doctor before delivery is less than 3000 grams. The researcher states the hypotheses as

$\mathrm{H}0:\mathrm{μ}=3000\text{grams}{H}_0:\mathrm{μ}=3000\text{grams}$

$\text{Ha:}\mathrm{μ}≤2999\text{grams}{H}_a:\mathrm{μ}≤2999\text{grams}$

Jump around Refer to Exercise 78.

a. Construct and interpret a $90\%$ confidence interval for the true mean vertical jump $\mathrm{μ}$(in inches) of the students at Haley, Jeff, and Nathan’s school. Assume that the conditions for inference are met.

b. Explain why the interval in part (a) is consistent with the result of the test in Exercise $78$

Fast connection? How long does it take for a chunk of information to travel

from one server to another and back on the Internet? According to the site

internettrafficreport.com, the average response time is 200 milliseconds (about one-fifth of a second). Researchers wonder if this claim is true, so they collect data on response times (in milliseconds) for a random sample of 14 servers in Europe. A graph of the data reveals no strong skewness or outliers.

a. State an appropriate pair of hypotheses for a significance test in this setting. Be sure to define the parameter of interest.

b. Check conditions for performing the test in part (a).

c. The 95% confidence interval for the mean response time is 158.22 to 189.64

milliseconds. Based on this interval, what conclusion would you make for a test of the hypotheses in part (a) at the 5% significance level?

d. Do we have convincing evidence that the mean response time of servers in the United States is different from 200 milliseconds? Justify your answer.

Water! A blogger claims that U.S. adults drink an average of five $8-$ounce glasses (that’s $40$ ounces) of water per day. Researchers wonder if this claim is true, so they ask a random sample of $24$ U.S. adults about their daily water intake. A graph of the data shows a roughly symmetric shape with no outliers.

a. State an appropriate pair of hypotheses for a significance test in this setting. Be sure to define the parameter of interest.

b. Check conditions for performing the test in part (a).

c. The $90\%$ confidence interval for the mean daily water intake is $30.35$ to $36.92$ ounces. Based on this interval, what conclusion would you make for a test of the hypotheses in part (a) at the $10\%$ significance level?

d. Do we have convincing evidence that the amount of water U.S. children drink per day differs from $40$ ounces? Justify your answer.

Tests and confidence intervals The $P-$value for a two-sided test of the null hypothesis $H_0:\mathrm{μ}=10$is$0.06$

a. Does the $95\%$ confidence interval for μ include $10$? Why or why not?

b. Does the $90\%$ confidence interval for μ include $10$? Why or why not?