Question

UPC The heights of 16 randomly selected girls entering Kindergarten are given below (in inches). The sign test at the 0.01 significance level will be used to test the claim that the population median is greater than 43 inches. 42 er 44 44.4 42.4 41.2 45.2 44.1 43 44.3 43 44.3 43 44.2 44 44.2 42.7 (a) What is the value of the test statistic used in this sign test? (b) What is the critical value in this sign test? (c) What is the correct conclusion of this sign test? There is not sufficient evidence to support the claim that the population median is greater than 43 inches. There is sufficient evidence to warrant rejection of the claim that the population median is greater than 43 inches. There is sufficient evidence to support the claim that the population median is greater than 43 inches.

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Answer 1

Solution:- Given that 42,44,44.4,42.4,41.2,45.2,44.1,43,44.3,43,44.3,43,44.2,44,44.2,42.7

X = 43.5, sd = 1.0633, n = 16

(a) The test statistic = 1.881

(b) The critical value = 2.602

(c) option D.

The provided sample mean is I = 43.5 and the sample standard deviation is s = 1.0633, and the sample size is n = 16. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: 1 = 43 Ha: 1 > 43 This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.01, and the critical value for a right-tailed test is te = 2.602. The rejection region for this right-tailed test is R=t:t> 2.602 (3) Test Statistics The t-statistic is computed as follows: X - t = 43.5 - 43 1.0633/16 = 1.881 (4) Decision about the null hypothesis Since it is observed that t = 1.881 <tc = 2.602, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p = 0.0398, and since p = 0.0398 > 0.01, it is concluded that the null hypothesis is not rejected. (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean I is greater than 43, at the 0.01 significance level.