Previously, the U.S. Census reported that the average family consists of 3.14 pe

Question

Previously, the U.S. Census reported that the average family consists of 3.14 persons with a standard deviation of 1.37 persons. In order to find out if the average has changed from the previous results, a sample of 5,000 families was collected with an average of 3.10 persons. The U.S. Census wants to be ninety-eight percent confident when they report if the average is now lower or if there has not been any significant change. a. Write the Null and Alternate Hypothesis b. What is alpha () in this scenario? c. Would you conduct a 1-tailed test (upper or lower) or a 2-tailed test? d. What critical value will you use to identify the rejection regions? e. Write the test statistic formula you should use f. Calculate the test statistic g. State your conclusion – Reject or fail to reject the null hypothesis h. What should the U.S. Census report per the results of this test? i. What is the p-value? j. To what should you compare the p-value to make a conclusion on this hypothesis test? k. What’s your conclusion based on the p-value and how did you decide?

Explanation / Answer

Given,

population mean (µ)=3.14

population SD=1.37

sample mean=3.10

sample size=5000

confidence interval=98%

A.a) Null hypothesis H0: µ3.14

Alternate hypothesis H1: µ<3.14

A.b) alpha() is termed as significance level

significance level()=100-98=2%

A.c) As the US census wants to report if the average is lower or not,

we use one tail test with lower tail test

A.d) we will calculate Z-score to identify rejection regions

A.e) Formula is given as

Z(calc)=(x- µ)/{SD/sqrt(n)}

A.f) Z(calc)={3.10-3.14}/{1.37/sqrt(5000)}

solving we get

Z(calc)=-2.064

A.g) from normal distribution table, we have

Z-table value =-2.055

as -2.055>-2.064

Z(calc) is outside the region of curve

hence we reject the null hypothesis

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