A student group claims that first-year students at a university must study 2.5 hours (150 minutes) per night during the school week. A skeptic suspects that they study less than that on the average. A class survey finds that the average study time claimed by 269 students is = 144 minutes, with a sample standard deviation of 70.
A) Regard these students as a random sample of all first-year students and suppose we know that the study times follow a Normal distribution. What is the standard error of the sample mean?
B) Consider the hypotheses H0: μ = 150 against Ha: μ < 150. What is the value of the test statistic? Give your answer to two decimal places.
A) The standard error of the sample mean can be calculated using the formula:
Standard Error = Sample Standard Deviation / Square Root of Sample Size
Given that the sample standard deviation is 70 and the sample size is 269, we can substitute these values into the formula to calculate the standard error:
Standard Error = 70 / √269 ≈ 4.27
Therefore, the standard error of the sample mean is approximately 4.27.
B) The test statistic can be calculated using the formula:
Test Statistic = (Sample Mean - Population Mean) / Standard Error
In this case, the sample mean is 144, the population mean is 150, and the standard error is 4.27. Substituting these values into the formula:
Test Statistic = (144 - 150) / 4.27 ≈ -1.40
Therefore, the value of the test statistic is approximately -1.40.
A) To find the standard error of the sample mean, we can use the formula:
Standard Error = (Sample Standard Deviation) / √(Sample Size)
Given that the sample standard deviation is 70 and the sample size is 269, we can substitute these values into the formula:
Standard Error = 70 / √269
Using a calculator, we can find the value of the standard error, which is approximately 4.26.
B) To calculate the test statistic, we need to use the formula:
Test Statistic = (Sample Mean - Population Mean) / (Standard Error)
In this case, the sample mean is 144 (given) and the population mean is 150 (stated in the hypothesis). The standard error is calculated in part A as approximately 4.26.
Substituting these values into the formula:
Test Statistic = (144 - 150) / 4.26
Using a calculator, we can find the value of the test statistic, which is approximately -1.41 (rounded to two decimal places).
Z = (144-150/Standard Error (SE) of the mean
SE = SD/sq rt of n-1
I hope this helps.