An economist wants to estimate the average amount in savings account at banks in a given region. A random sample of 100 accounts gives a mean of $ 357.60 and standard deviation of $ 1.40. (1) Given a 95% confidence interval for the average amount in any savings accounts at a bank in the given region.

A half-century ago, the mean height of women in a particular country in their 20s was 62.4 inches. Assume that the heights of today's women in their 20s are approximately normally distributed with a standard deviation of 1.67 inches. If the mean height today is the same as that of a half-century ago, what percentage of all samples of 27 of today's women in their 20s have mean heights of at least 63.02 inches? About% of all samples have mean heights of at least 63.02 inches. (Round to one decimal place as needed.)

A car company claims that its new SUV gets better gas mileage than its competitor's SUV. A random sample of 49 of its SUVs has a mean gas mileage of 17.1 miles per gallon (mpg). The population standard deviation is known to be 1.3 mpg. A random sample of 33 competitor's SUVS has a mean gas mileage of 16.3 mpg. The population standard deviation for the competitor is known to be 1.6 mpg. Test the company's claim at the 0.05 level of significance. Let the car company be Population 1 and let the competitor be Population 2. Step 2 of 3: Compute the value of the test statistic. Round your answer to two decimal places.

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.)

A nurse is interested in the amount of time patients spend exercising per day. According to a recent study, the daily workout time per adult follows an approximately normal distribution with a mean of 94 minutes and a standard deviation of 27minutes. If the nurse randomly samples patients in her office to analyze their exercise time and gets a standard error of 3minutes, how many patients did she sample?

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 non-symmetric dataset has a mean of 200 and a standard deviation of 15.  Find an upper bound for the proportion of data points that are either greater than 230 or less than 170.

Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.4 and a standard deviation of 1.51. Using the empirical rule, what percentage of American women have shoe sizes that are between 5.38 and 11.42?

An educational consulting group claims that there is a difference in the mean student loan debt of students who attended private four-year colleges and the mean student loan debt of students who attended out-of-state public four-year colleges. Student loan debt of 10 randomly selected students who attended private four-year colleges and 10 randomly selected students who attended out-of-state public four-year colleges, at the time of graduating college, are recorded. Assume that the population standard deviation of student loan debt is $5,000 for both the private college attendees and the public college attendees, and assume that the distribution of student loan debt is normally distributed for both the private college attendees and the public college attendees. Let the students who attended private four-year colleges be the first sample, and let the students who attended out-of-state public four-year colleges be the second sample. The group conducts a two-mean hypothesis test at the…

Oil wells in a large fiels produce an average of 33.5 barrels per day. Fifteen randomly selected oil wells produce an average of 30 barrels of crude oil per day with a standard deviation of 3.5 barrels. Is there enough evidence to conclude that the oil wells are not producing an average of 33.5 barrels of crude oil per day. Test at a=0.01.use two tailed.