Question

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27) 2 points At engineering faculty, it is estimated that at most 25% of the students ride bicycles to class. Does this seem to be a valid estimate if, in a random sample of 90 college students, 28 are found to ride bicycles to class? Use a 0.05 level of significance.

Answer 1

The following information is provided: The sample size is N = 90, the number of favorable cases is X = 28, and the sample proportion is p = * = 28 = 0.3111, and the significance level is a = 0.05 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho:p < 0.25 Ha:p > 0.25 This corresponds to a right-tailed test, for which a z-test for one population proportion needs to be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the critical value for a right-tailed test is ze = 1.64. The rejection region for this right-tailed test is R = + {z:z > 1.64} (3) Test Statistics The z-statistic is computed as follows: z = P - po v po(1 – po)/n 0.3111 - 0.25 0.25(1 – 0.25)/90 = 1.339 (4) Decision about the null hypothesis 1.64, it is then concluded that the null Since it is observed that z = 1.339 < Zc hypothesis is not rejected. Using the P-value approach: The p-value is p = 0.0903, and sincep = 0.0903 0.05, 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 proportion p is greater than po, at the a = 0.05 significance level. Confidence interval The 95% confidence interval for p is: 0.215 < p < 0.407. Graphically Z-Test Results: Z-stats = 1.339, p-value =0.0903 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -4.0 -3.5 -3.0-2.5 -2.0-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

yes, claim is valid.

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