Q1: A business school placement director wants to estimate the mean annual salaries 5 years after students graduate. A random sample of 25 such graduates found a sample mean of $42,740 and a sample standard deviation of $4,780. Find a 90% confidence interval for the population mean, assuming that the population distribution is normal.

A random sample of 500 observations yields x̅ =400 and s=50. What is the  95% confidence interval for the population mean?

Assume that the heights of women are normally distributed. A random sample of 20 women have a mean height of 62.5 inches and a standard deviation of 1.3 inches. Construct a 98% confidence interval for the population variance, .

In a random sample of 5 mobile​ devices, the mean repair cost was ​$60.00 and the standard deviation was ​$12.00. Assume the population is normally distributed and use a​ t-distribution to find the margin of error and construct a 95​% confidence interval for the population mean. Interpret the results.

Suppose a sample of 30 students are given an IQ test. The sample has a standard deviation of 12.23 points. Assuming IQ test score follow a normal distribution, suppose the researcher wishes to obtain a 90% confidence interval for the population standard deviation.

The mean number of English courses taken in a two-year time period by male and female college students is believed to be about the same. An experiment is conducted and data are collected from 29 males and 16 females. The males took an average of three English courses with a standard deviation of 0.8. The females took an average of four English courses with a standard deviation of 1.0. Are the means statistically the same? (Assume a 5% level of significance.)

In a random sample of 17 people, the mean commute time to work was 30.2 minutes and the standard deviation was 7.1 minutes. Assume the population is normally distributed and use a t- distribution to construct a 95% confidence interval for the population mean y. What is the margin of error of y? Interpret the results.

In a school district, all sixth grade students take the same standardized test. The superintendant of the school district takes a random sample of 3030 scores from all of the students who took the test. She sees that the mean score is 169169 with a standard deviation of 7.06747.0674. The superintendant wants to know if the standard deviation has changed this year. Previously, the population standard deviation was 1313. Is there evidence that the standard deviation of test scores has decreased at the α=0.005α=0.005 level? Assume the population is normally distributed. Step 1 of 5:  State the null and alternative hypotheses. Round to four decimal places when necessary. Step 2 of 5:  Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.     Step 3 of 5:  Determine the value of the test statistic. Round your answer to three decimal places. Step 4 of 5:  Make the…

A large financial company employs a human resources mamanger who is in charge of employe benefits. The manger wishes to estimate the average dental expenses per employee for the company. She selects a random sample of 60 employee records for the past year and determines that the sample mean of $492. Moreover, it is known from past studies that the population standard deviation for annual dental expenses is $74. Use this data to calculate a 95% cofidence interval for the mean expenses of all employees.

In September a biological research team caught, weighed, and released a random sample of 24 chipmunks in Rocky Mountain National Park. The mean of the sample weights was x-bar = 8.7 oz. with sample standard deviation s = 1.4 oz. Find a 90% confidence interval for the mean September weight of all chipmunks in Rocky Mountain National Park.