V According to a report done last year by the dental industry, 82% of dentists would recommend Starry Whites toothpaste. After some recent negative publicity, the sales team at Starry Whites suspects the proportion of dentists who now recommend the brand is lower. The team chooses 145 dentists at random and asks them whether they'd recommend the brand. Of those, 108 say they'd recommend it. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0,10 level of significance, to conclude that the proportion, p, of all dentists who now recommend this brand is less than 82%. (a) State the null hypothesis /, and the alternative hypothesis #, that you would use for the test. H: I 020 0-0 0*0 (b) For your hypothesis test, you will use a Z-test. Find the values of ap and # (1-p) to confirm that a Z-test can be used. (One standard is that mp 2 10 and m (1-p)2 10 under the assumption that the null hypothesis is true.) Here , is the sample size and p is the population proportion you are testing ? " (1-P)=0 (c) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. . The value of the test statistic is given by - P -P P (I- P ) . The p-value is the area under the curve to the left of the value of the test statistic. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. o One-tailed O Two-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) Step 3: Shade the area represented by the p- value Step 4: Enter the p- value. (Round to 3 decimal places.) ? (d) Based on your answer to part (c), choose what can be concluded, at the 0.10 level of significance, about the proportion of all dentists who now recommend the brand. X ? ce the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to conclude that less than 82% of all dentists now recommend the brand. Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to conclude that less than 82% of all dentists now recommend the brand. Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to conclude that less than 82% of all dentists now recommend the brand. Since the p-value is greater than the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to conclude that less than 82%% of all dentists now recommend the brand. Explanation Check