Question

please answer all

1.       A study showed that in a certain month, the mean time spent per visit to Facebook was 19.5 minutes. Assumes the standard deviation of the population is 8 minutes. Suppose that a simple random sample of 100 visits in that month has a sample mean of 21.35 minutes. A social scientist is interested in knowing whether the mean time of Facebook visits has increased. Perform the hypothesis test and compute the P-value.

Based on the P value, what is the conclusion we test at 0.05 level significance?

2.       A random sample of 64 second graders in a certain school district are given a standardized mathematics skills test. The sample mean score is 51.93. Assume the standard deviation for the population of test scores is 15. The nationwide average score on this test is 50. The school superintendent wants to know whether the second graders in her school district have greater math skills than the nationwide average. Perform the hypothesis test and compute the P value.

Based on your P value, what is the conclusion if we test at 0.05 level of significance?

3.       Suppose that the mean price of a home in Denver, Colorado in 2008 was 225.3 thousand dollars. A random sample of 49 homes sold in 2010 had a mean price of 200.8 thousand dollars. A real estate firm wants to test to see if the mean price of 2010 differs from the mean price in 2008. Assume that the population standard deviation is 140. Perform the hypothesis test and compute the P value.

Based on your P value, what is the conclusion if we test at the 0.05 level of significance?

Answer 1

Question 1:

As we are trying to test here whether  the mean time of Facebook visits has increased, therefore the null and the alternate hypothesis here are given as:

The test statistic here is computed as:

Now as this is a one tailed test, we get from the standard normal tables:

p = P(Z > 2.3125) = 0.0104

Now as the p-value here is 0.0104 < 0.05 which is the level of significance, therefore the test is significant and we can reject the null hypothesis here and conclude that  the mean time of Facebook visits has increased.