Question

To step Tro 07:30 A salesman for a new manufacturer of cellular phones claims not only that they cost the retailer less but also that the percentage of defective cellular phones found among his products. (Pi ). will be no higher than the percentage of defectives found in a competitor's line. (P2). To test this statement, the retailer took a random sample of 130 of the salesman's cellular phones and 105 of the competitor's cellular phones. The retailer found that 12 of the salesman's cellular phones and 7 of the competitor's cellular phones were defective. Does the retailer have enough evidence to reject the salesman's claim? use a significance level of ?-0.05 for the test. Step 1 of 6:State the null and alternative hypotheses for the test. Answer 2 Points KeypadTables Ho: pi

Answer 1

For sample 1, we have that the sample size is i130, the number of favorable cases is XI = 12, so then the sample proportion is pl = 0.0923 For sample 2, we have that the sample size is N2 - 105, the number of favorable cases is X2 7, so then the sample proportion is 2167 The value of the pooled proportion is computed as 105 1-m-130-105-0.0809 Also, the given significance level is α-0.05 The following null and alternative hypotheses need to be tested This corresponds to a left-tailed test, for which a z-test for two population proportions needs to be conducted (2) Rejection Region Based on the information provided, the significance level is α 0.05, and the critical value for a left-talled test is zc--1.64 The rejection region for this left-tailed test is R {z : z <-1.64) The z-statistic is computed as follows P1 p2 0.0923 - 0.0667 P(1 P)(1/ni + 1/n2) /0.0809 (1-0.0809) (1/130 +1/105) 4) Decision about the null hypothesi Since it is observed that z 0.717 2 zc1.64, it is then concluded that the null hypothesis is not rejected Using the P-value approach: The p-value is p- 0.7633, and since p-0.7633 > 0.05, it is concluded that the null hypothesis is not rejected It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportlon pi is less than p2, at the 0.05 significance level The 95% confidence interval for pi-P2 is:-0.043 < pi-P2 < 0.095