sampling distribution

The average annual salary in a district is $30,000. Assuming that the salaries were normally distributed for a certain group of wage earners with a standard deviation of $5,000, what is the probability that for a randomly selected sample of 70 earners the mean salary falls below..

The university authorities wanted to estimate the average age of the students in their university by taking a random sample of 25 students. The standard deviation was found to be 3 years. Find the 95% confidence interval for the variance (σ 2 ) and standard deviation (σ). Assu..

Past records indicated that the variance of scores in final exams of the high school students was 6.16. New techniques were adopted for teaching and it was observed that in a random sample of 80 students, the variance of scores after the final exam is 6.42. Find the chi-square test value...

A survey on hospitals concluded that the standard deviation of the amount of time a patient has to wait before being attended by emergency room personnel is more than 5.4 minutes. Waiting times in the case of a sample of 16 patients are recorded and it was found that the standard deviatio..

The standard deviation of carbohydrates in a random sample of 15 different kinds of 4 oz patty sandwitches is 5.4 grams. At α = 0.01, test the hypothesis that the standard deviation is greater than 4.8 grams. What is the chi-square test value? [Assume that the variable is normally h..

A sample of 10 mathematics books of grade 7 had the following number of pages. Find the 98% confident interval for the variance of the pages. Assume that the variable is normally distributed. 1000 1320 590 820 1150 1570 1090 1585 995 1285 => between 38110 and 345769 or between 4..

A consumer claims that the standard deviation of the quantity of softdrink in a bottle is more than 0.23 oz. The researcher of the company selected a sample of 10 bottles and found the standard deviation as 0.32 oz. Find the P -value for the test. At α = 0.05, is there enough eviden..

The life expectancy (years) at birth of a random sample of 20 countries is shown here. Find the 99% confidence interval for the standard deviation. Assume that the variable is normally distributed. 77 67 76 69 60 57 59 55 57 53 54 50 51 49 50 49 72 69 50 48 => between 6.65 and 1..

The weight (in grams) of a sample of 50 eggs are as shown in the frequency distribution table. Weight Frequency 80 - 84 2 85 - 89 6 90 - 94 12 95 - 99 14 100 - 104 10 105 - 109 5 110 - 114 1 Find the variance and standard deviation. => 6.85 and 2.62 or 96.3 and 9319.7 or 46.95 a..

The snowfall (in inches) from a random sample of 10 counties in U.S. in the month of January are as follows. 3 5 4 2 4 6 2 2 1 4 At α = 0.05, test the hypothesis that the standard deviation of snowfall is less than 2.8 inches. What is the chi-square test value? [Assume that the vari..