A random sample of size 16 has 53 as mean. The sum of squares of deviations from mean is 150. Can this sample be regarded as taken from the population having 56 as mean ? Also obtain 95% confidence limits for the mean. (t1s = 2.131, 16 =2-602)

The sample mean of depression scores of 16 fifth graders was 4.4 with standard deviation of 8. If the population mean of this depression score is 6, what is the calculated t score for this sample?

A random sample of 100 observations from a quantitative population produced a sample mean of 28.0 and a sample standard deviation of 6.5. Use the p-value approach to determine whether the population mean is different from 31.

P3. Show that the mle of unknown standard deviation when the mean is known is different from the sample standard deviation when the random sample is taken from a normal population characterized by two parameters, mean and variance. Which estimator is unbiased? Justify your answer. Show that a sample mean is a minimum variance unbiased estimator of the mean of a normal population with known variance.

Forty refrigerators from two different models of a refrigerator manufacturer are compared to see if the smaller model uses less energy than the larger model. The energy was measured in kilowatt hours per month (kwh/mo). From years of testing these models, it is known that the standard deviation of kwh/mo is 34 kwh/mo for the smaller model and 40 kwh/mo for the larger one. From this survey, the sample means and standard deviations are 125 and 34, and 90 and 40, respectively. If we conduct a hypothesis test, the decision and conclusion are   Group of answer choices   Do not reject the null hypothesis and conclude that the average kwh/mo are the same.   Reject the null hypothesis and conclude that the average kwh/mo are different.   Reject the null hypothesis and conclude that the average kwh/mo for the smaller refrigerator is higher than for the larger model.   Do not reject the null hypothesis and conclude that the average kwh/mo for the smaller refrigerator is higher than for…