Exam 8: Inferences From Samples to Populations

A laboratory tested 83 chicken eggs and found that the mean amount of cholesterol was 181 milligrams with S = 11.6 milligrams. Use a single value to estimate the mean amount of cholesterol for all chicken eggs.

Solve the problem. -Suppose you know that the distribution of sample proportions of fifth grade students in a large school district who read below grade level in samples of 100 students is normal with a mean of 0.30 and a standard deviation of 0.05. You select a sample of 100 fifth grade students from this district and find that the proportion who read below grade level in the sample is 0.33. How many standard deviations is the sample proportion above or below the mean of the distribution of sampling proportions?

Find an estimate of the sample size needed to obtain the specified margin of error for the 95% confidence interval of a population mean. -Margin of error $= 0.08$ , sample standard deviation $= 1.4$

A researcher wishes to estimate the mean height of women aged between 60 and 65 in the U.S. She desires a margin of error of 0.1 inches. Past studies suggest that a population standard deviation of 3.3 inches is reasonable. 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. -When 12 long-distance runners were randomly selected and tested, a mean resting heart rate of 70.0 beats per minute was obtained. Based on this sample statistic, what is the best estimate for the mean resting heart rate for all long-distance runners?

The college daily reported: "450 students living in university housing were polled. 270 said that they were satisfied with their living conditions. Based on this survey we conclude that 60% of students living in dormitories are satisfied. The margin of error of the study is 5 percentage points (with a 95% degree of confidence). Which statement is correct?

Solve the problem. Round your answer to one decimal place, if necessary. -A random sample of 30 long distance runners aged 20-25 was selected from a running club. The resting heart rates (in beats per minute)of the runners are shown below. Find the 95% confidence interval for the mea resting heart rate for the population of long distance runners aged 20-25. 62 70 61 64 75 54 72 68 74 54 75 70 62 66 79 73 81 60 66 76 67 62 71 68 62 86 76 60 53 71 62 70 61 64 75 54 72 68 74 54 75 70 62 66 79 73 81 60 66 76 67 62 71 68 62 86 76 60 53 71

A medical researcher wishes to estimate what proportion of babies born at a particular hospital are born by caesarean section. In a random sample of 64 births at the hospital, 26% were Caesarean sections. Find the margin of error for the 95% confidence interval.

In a survey of high school students, 1100 students were randomly selected from California, and the proportion who spoke a second language in addition to English was 0.15. Based on that sample statistic, what is the best Estimate of the proportion for all high school students in California?

Find an estimate of the sample size needed to obtain the specified margin of error for the 95% confidence interval of a population mean. -Margin of error $= 0.90$ , sample standard deviation $= 9$

Solve the problem. -Suppose you know that the distribution of sample proportions of the residents of one town over 70 years old in samples of 120 residents is normal with a mean of 0.12 and a standard deviation of 0.04. You select a sample of 120 residents and find that the proportion of residents over 70 is 0.02. What is the probability that a second sample would be selected with a proportion greater than 0.02?

Solve the problem. Round your answer to one decimal place, if necessary. -The distribution of sample means for a group of test scores for samples of 100 scores is normal with a mean of 63.9 and a standard deviation of 1.8. Suppose you take a sample of 100 test scores and find that the mean is 65.5. How many standard deviations is the sample mean from the mean of the distribution of sample means?

Find an estimate of the sample size needed to obtain the specified margin of error for the 95% confidence interval of a population mean. -Margin of error $= 6.3$ , sample standard deviation $= 18$

A poll of 1000 voters in one district showed that 62% of them would favor stricter gun control laws. Find the margin of error for the 95% confidence interval for this study.

Solve the problem. Round your answer to one decimal place, if necessary. -The distribution of sample means for a group of test scores for samples of 100 scores is normal with a mean of 61.2 and a standard deviation of 1.7. Suppose you take a sample of 100 test scores and find that the mean is 59.3. How many standard deviations is the sample mean from the mean of the distribution of sample means?

Solve the problem. Round your answer to the nearest whole number unless indicated otherwise. -An economist wants to estimate mean annual income for recent college graduates majoring in statistics. how many such incomes must be found if he wants to be 95% confident that the sample mean is within $500 of the true population mean? Assume that a previous study has revealed that for such incomes $\sigma = \$ 5250$

Solve the problem. Round your answer to one decimal place, if necessary. -The distribution of sample means for monthly employee income at a particular company for samples of 70 employees is normal with a mean of $5587 and a standard deviation of $220. You take a random sample of 70 employees from the company and find that their mean monthly income is $5837. How many standard deviations is the sample mean from the mean of the sampling distribution?

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 $= 3025$ , sample proportion $= 0.89$

There are 13,427 eligible voters in one town. In a sample of 825 eligible voters from this town, the proportion who say that they plan to vote in the next mayoral election is 0.48 . Based on that sample statistic, what is the best estimate of the proportion for all eligible voters in the town?

Solve the problem. Round your answer to one decimal place unless otherwise indicated. -Physiologists often use the forced vital capacity as a way to assess a person's ability to move air in and out of their lungs. A researcher wishes to estimate the forced vital capacity of people suffering from asthma. When 15 asthmatics were randomly selected and tested for their forced vital capacity, a mean forced vital capacity was obtained of 4.4 liters. Based on this sample statistic, what is the best estimate of the mean forced vital capacity For all asthmatics?