Exam 8: Inferences From Samples to Populations

A population proportion is to be estimated from the sample described. Approximate the 95% confidence interval. Round your answer to four decimal places, if necessary. -A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 520 college students showed that $16 \%$ of them had, or intended to, cheat on examinations. Find the $95 \%$ confidence interval.

Solve the problem. Round your answer to one decimal place unless otherwise indicated. -A researcher for a car insurance company wishes to estimate the mean annual premium that men aged 20-24 pay for their car insurance. When 16 men aged between 20 and 24 were randomly selected and surveyed on their annual car insurance premiums, a mean of $760 was obtained. Based on this sample statistic, what is the best estimate of the mean annual car insurance premium for all men aged between 20 and 24? Round your answer to the nearest dollar.

Solve the problem. Round your answer to one decimal place unless otherwise indicated. -Ten apples of a particular variety are selected at random and weighed. The weights (in ounces)are as follows: $8.5,7.8,8.1,6.9,7.4,6.1,7,8.6,8.3,7.9$ Estimate the mean weight of all apples of this variety.

Eleven female college students are selected at random and asked their heights. The heights (in inches)are as follows: $68,59,65,71,64,63,68,63,61,65,62$ Estimate the mean height of all female students at this college.

A population proportion is to be estimated. Estimate the minimum sample size needed to achieve the specified margin of error with a 95% degree of confidence. -A researcher wishes to estimate the proportion of children in a certain neighborhood who are living with only one parent. She wishes to achieve a margin of error of E = 0.021. What is the minimum sample size needed?

The weights (in pounds)of a random sample of 32 new born babies, born at a particular hospital are given below. Find The 95% confidence interval for the mean weight of the population of new born babies born at this hospital. 7.5 6.4 7.1 7.1 6.8 8.6 7.4 6.4 7.4 7.0 6.0 7.8 9.0 7.3 6.5 5.8 8.4 7.6 7.2 6.5 8.5 7.1 6.3 6.9 7.0 5.9 8.3 6.6 7.3 7.7 6.4 8.2

Solve the problem. -Among a random sample of 250 college students, the mean number of hours worked per week at non-college related jobs is 14.2. This mean lies 2 standard deviation(s)above the mean of the sampling distribution. If a second sample of 250 students is selected, what is the probability that for the second sample, the mean number Of hours worked will be greater than 14.2?

Solve the problem. Round your answer to one decimal place unless otherwise indicated. -A long-distance phone company wishes to estimate the mean duration of long-distance calls originating in california. A random sample of 15 long-distance calls originating in California yields the following call durations, in minutes. 1 3 2 1 4 23 40 24 16 31 1 19 12 2 37 Use the data to obtain an estimate of the mean call duration for all long-distance calls originating in California.

The mean of the sample means is 267 pounds. Yes, both means equal 267 pounds. -An employee at the local company is attending night school to get a better job. In the fall term, she took 4 courses, in the winter term she took 5 courses, and in the spring term she took 6 courses. Consider the values of 4, 5, and 6 to be a population. Assume that samples of size 2 are randomly selected with replacement from the population of number of courses. Find the mean of each of the 9 different samples. Is the mean of the sampling distribution equal to the mean of the population of the three listed values?

Find the population proportion or sample proportion as indicated. Round your answer to two decimal places, if necessary. -Of the 2281 students at a liberal arts college, 250 are fifth year students. Among a sample of 326 of the students from this college, 33 are fifth year students. Find the population proportion of fifth year students.

Sample size $= 256$ , sample mean $= 40$ , sample standard deviation $= 13$ What is the $95 \%$ confidence interval for the population mean?

A mayoral election race is tightly contested. In a random sample of 1300 likely voters, 676 said that they were planning to vote for the current mayor. Based on this sample, would you claim that the mayor will win a majority of the votes? Explain.

Solve the problem. -Among a random sample of 500 college students, the mean number of hours worked per week at non-college related jobs is 15.1. This mean lies 2.8 standard deviation(s)below the mean of the sampling distribution. If a second sample of 500 students is selected, what is the probability that for the second sample, the mean number oOf hours worked will be at least 15.1?

There are 310 teachers at a college. In a sample of 118 teachers from this college,the proportion who had doctorates was 0.55. Based on that sample statistic, what is the best estimate of the proportion for all teachers at This college?

Solve the problem. Round your answer to the nearest whole number unless indicated otherwise. -A government survey conducted to estimate the mean price of houses in a metropolitan area is designed to have a margin of error of $10,000. Pilot studies suggest that the population standard deviation is $40,000. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.

Solve the problem. Round your answer to one decimal place unless otherwise indicated. -A sample of nine students is selected from among the students taking a particular exam. The nine students were asked how much time they had spent studying for the exam and the responses (in hours)were as follows: $17,7,9,14,11,16,6,19,22$ Estimate the mean study time of all students taking the exam.

There are 13,417 eligible voters in one town. In a sample of 802 eligible voters from this town, 386 say that they plan to vote in the next mayoral election. Based on this sample statistic, estimate the number of eligible voters in this town who will not vote in the next mayoral election.

There are 2030 students in a school district. In a sample of 483 students from this school district, 164 have mathematics scores below grade level. Based on this sample statistic, estimate the number of students in this school district with mathematics scores below grade level.

The distribution of sample means for scores on a test for samples of size 100 is normal with a mean of 61.7 and a standard deviation of 1.5. If a sample of 100 test scores is selected at random, what is the probability that the sample mean will be greater than 63.8?

A sample of 100 statistics students at a small college had a mean mathematics ACT score of 28 with a standard deviation of 7. Use a single value to estimate the mean mathematics ACT score for all statistics students.