Exam 8: Inferences From Samples to Populations

Solve the problem. Round your answer to one decimal place, if necessary. -A random sample of 30 seventh grade students was selected from a particular school district. The students were asked how many siblings they had. The responses are given below. Find a 95% confidence interval for the mean number of siblings for the population of seventh grade students in this school district. 0 2 1 1 3 2 0 0 1 4 3 1 2 0 1 1 6 4 1 1 1 0 5 1 4 2 2 1 0 2

A population mean is to be estimated from the sample described. Round your answer to one decimal place if necessary. Assume that all confidence intervals use a 95% confidence level. -Sample size = 256, sample mean = 45, sample standard deviation = 17 What is the margin of error?

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 left handed people among a certain population. In a random sample of 1000 people from the population, $61.9 \%$ are left-handed. Find the $95 \%$ confidence interval for the population proportion of left-handed people.

There are 2221 students in a school district. In a sample of 452 students from this school district, 161 have mathematics scores below grade level. Based on this sample statistic, estimate the population proportion of students in this district with mathematics scores below grade level.

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. -Sample size $= 225$ , sample proportion $= 0.9$

Provide an appropriate response. -In a poll of 2490 voters in a certain city, 71% said that they backed a bill which would limit growth and development in their city. The margin of error in the poll was reported as 2 percentage points (with a 95% degree of confidence). Which statement is correct?

A sample of 81 statistics students at a small college had a mean mathematics ACT score of 24 with a standard deviation of 8 . Find the $95 \%$ confidence interval. Round your answer to two decimal places.

Margin of error $= 0.06$ , sample size $= 50$ , sample mean $= 0.65$ What is the $95 \%$ confidence interval for the population mean?

A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 550 college students showed that 22% of them had, or intended to, cheat on examinations. Find the margin of error for the 95% confidence interval.

In one city, there are a total of 1698 5-year-old children of whom 559 live with one parent only. Among a sample of 603 of the 5-year-old children from this city, 229 live with one parent only. Find the sampleproportion of 5-year-old children who live with only one parent.

A sample of 400 employees from a particular software company had a mean monthly income of $\$ 7288$ with a standard deviation of $\$ 2763$ . Find the $95 \%$ confidence interval. Round your answer to the nearest dollar.

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. - $E = 0.05$

Among a sample of 76 students selected at random from one college, the mean number of siblings is $1.5$ with a standard deviation of $1.2$ . Find the $95 \%$ confidence interval. Round your answer to two decimal places.

The college daily reported: "278 students living in university housing were polled. One hundred and sixty-four said that they were satisfied with their living conditions. Based on this survey we conclude that 59% of students living in dormitories are satisfied. The margin of error of the study is 6 percentage points." Which statement is correct?

Solve the problem. -Among a random sample of 150 employees of a particular company, the mean commute distance is 25.4 miles. this mean lies 1.7 standard deviation(s)below the mean of the sampling distribution. In a second sample of 150 employees selected from the same company, the mean commute distance is 31.7 miles. This second sample mean lies 2 standard deviation(s)above the mean of the sampling distribution. If a third sample of 150 employees is selected, what is the probability that the sample mean will lie between 25.4 and 31.7?

There are 328 teachers at a college. In a sample of 111 teachers from this college, 75 have doctorates. Based on this sample statistic, estimate the number of teachers at this college without doctorates.

In one city, there are a total of 1783 5 year old children of whom 560 live with one parent only. Among a sample of 605 of the 5 year old children from this city, 229 live with one parent only. Find the population proportion of 5 year olds who live with only one parent.

There are 2140 students in a school district. In a sample of 449 students from this school district, 169 have mathematics scores below grade level. Based on this sample statistic, estimate the number of students in this school district with mathematics scores at or above grade level.

Nine employees of a company are selected at random and asked how far they commute to work each day. The distances (in miles)are as follows: $34,16,42,26,22,36,6,47,11$ Estimate the mean commute distance of all employees of the company.

A population proportion is to be estimated from the sample described. Approximate the margin of error for the 95% confidence interval. Round your answer to four decimal places, if necessary. -Sample size $= 256$ , sample proportion $= 0.5$