Exam 6: Putting Statistics to Work

Solve the problem. -The weights, in pounds, of twelve apples are given below. Find the mean weight. Round your answer to the nearest thousandth of a pound. 0.27 0.33 0.36 0.25 0.25 0.31 0.33 0.28 0.30 0.36 0.34 0.30

Answer the question. -Tell which of the following distributions would have the least variation.

Find the mode(s)for the given sample data. - $80,48,32,48,29,80$

Solve the problem. -Scores on a test are approximately normally distributed with a mean of 70 and a standard deviation of 9. The teacher wants to give A's to the top 10% of students, B's to the next 25%, and C's to the Next 42%. What is the bottom cutoff for a C grade? Round your answer to the nearest whole Number.

Find the range for the given data. -Jeanne is currently taking college economics. On the past five quizzes, Jeanne got the following scores. 5 17 3 14 10

Find the standard score for the given data value. -A data value in the 16th percentile.

For the given data value, find the standard score and the percentile. -A data value $2.3$ standard deviations below the mean.

A hypothesis test is to be performed. State the null and alternative hypotheses. -At one school, the average amount of time that tenth-graders spend watching television each week is $21.6$ hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased.

A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the givensituation. -Carter Motor Company claims that its new sedan, the Libra, will average better than 22 miles per gallon, which is the gas mileage of its competitor. The hypotheses are as follows: Null hypothesis: mean gas mileage $= 23 \mathrm { mpg }$ Alternative hypothesis: mean gas mileage $> 23 \mathrm { mpg }$

Solve the problem. -Scores on a test are approximately normally distributed with a mean of 70 and a standard deviation of 9. The teacher wants to give A's to the top 10% of students, B's to the next 25%, C's to the next 40%, D's to the next 16%, and F's to the bottom 9%. What is the bottom cutoff for a D grade? Round Your answer to the nearest whole number.

Find a 95% confidence interval for the true population proportion. -During the questioning of 78 potential jury members, $37 \%$ said that they had already formed an opinion as to the guilt of the defendant.

Select the requested distribution. -Which of the distributions is multimodal and approximately symmetric?

Find a 95% confidence interval for the true population proportion. -In a survey of 415 adults, 59% said that they favored the proposed environmental laws.

Use the range rule of thumb to approximate the standard deviation. -The race speeds for the top eight cars in a 200 -mile race are listed below. Round results to the nearest tenth.

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. -The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The diameters of the rolls (in m)are listed below. Compute the standard deviation. 0.45 0.558 0.644 0.145 0.627 0.268 0.294

Identify the distribution as symmetric, left-skewed, or right-skewed. -Amount of credit card debt of families in the U.S.

The result of a hypothesis is described in terms of the probability of obtaining a particular sample. Use the given contextto formulate the null and alternative hypotheses. Discuss whether the sample provides evidence for rejecting the nullhypothesis. -In the city of Heathville, the proportion of births that are by Caesarean section is $0.23$ (23\%). A small private hospital claims that at their hospital, the proportion of Caesarean births is lower. In a random sample of 120 births at the private hospital, the proportion of Caesarean births was $0.18$ . Assuming that the true proportion of Caesarean births at the private hospital is $0.23$ , the probability of selecting a sample in which the proportion of Caesareans is $0.18$ or less is roughly $0.09$ .

Provide an appropriate response. -Suppose that the proportion of left handers in a certain population is $0.1 ( 10 \% )$ . If samples of size 100 are repeatedly drawn from this population and the proportion of left handers in each sample is recorded, what can you say about the distribution of the sample proportions?

State how many peaks you would expect for the distribution described. -Number showing when a single die is rolled 100 times

Find a 95% confidence interval for the true population proportion. -In a random sample of 250 births at one hospital, 34% were by Caesarean section.