Researchers measured skulls from different time periods in an attempt to determi

Question

Researchers measured skulls from different time periods in an attempt to determine whether interbreeding of cultures occurred. Results are given below. Assume that both samples are independent simple random samples from populations having normal distributions. Use a 0.05 significance level to test the claim that the variation of maximal skull breadths in 4000 B.C. is the same as the variation in A.D. 150. 4000 B.C. 30 31.24 mm 5.15 mm A.D. 150 30 36.73 mm 5.36 mm What are the null and alternative hypotheses A. Hn: Ho: o 1 02 H1: Ge 20 H1: or Ho: H1: Identify the test statistic. F Round to two decimal places as needed.) Use technology to identify the P-value. The P-value is Round to three decimal places as needed

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis H0: A2 = B2

Alternative hypothesis HA: A2 B2

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data. Using sample data, the degrees of freedom (DF), and the test statistic (F).

DF1 = n1 - 1 = 30 -1

D.F1 = 29

DF2 = n2 - 1 = 30 -1

D.F2 = 29

Test statistics:-

F = 0.9232

Since the first sample had the smaller standard deviation, this is a left-tailed test.

p value for the F distribution = 0.42

Interpret results. Since the P-value (0.42) is greater than the significance level (0.05), we have to accept the null hypothesis.

Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that the variation of maximal skull breadths in 4000 B.C is the same as the variation in A.D. 150.

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