Stats II Assignment 2 Please answer all questions with the required calculations

Question

Stats II Assignment 2

                              Please answer all questions with the required calculations:

1.The UMES bookstore tells prospective students that the average cost of its statistics textbooks is $52 with a standard deviation of $4.50. A group of smart statistics students thinks that the average cost is higher. In order to test the bookstore’s claim against their alternative, the students selected a random sample of size 100. Assume that the mean price from their random sample is $52.80.

Using 5% level of significance, perform a hypothesis test using both the test statistic and the         P-value approach. What is the interval estimate?

2. Waste chemical pollutant in the Delmarva River has been constant for several years with a mean = 34 and standard deviation = 8. A group of factory representatives whose companies discharge the waste into the river is now claiming that they have lowered the average with improved filtration devices. A group of environmentalists want to test to see if this is true at the 5% level of significance.

Assume that their sample of size 50 gives a mean of 32.5. . Perform a hypothesis test using both the P-value and the test statistic approach. What is the interval estimates?

Explanation / Answer

2.

Ho: Mu < 34

ha: Mu>=34

Pop, Mean = 34

Sample mean = 32.5

Sigma = 8

n = 50

Test statistic = (32.5-34)/(8/sqrt(50)) = 1.33

The critical stat = 1.645

Now, since test statistic is less than critical statistic we conclude that we can't reject null hypothesis.

p-value is .9082, the critical pvalue is .95. Again, p-value is less than .95 so we can't reject null hypothesis

Interval estimates = Xbar +/- Z*Sigma/sqrt(N) = 34 +/- 1.645*8/sqrt(50) = 32.13 to 35.86

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