Question

(4 points) A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS of n = 1400 registered voters and found that 720 would vote for the Republican candidate. Let p represent the proportion of registered voters in the state who would vote for the Republican candidate. We test Hop=.50 H.:P > .50 (a) What is the 2-statistic for this test? (b) What is the P-value of the test? (6 points) A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 50 women over the age of 50 used the new cream for 6 months. Of those 50 women, 30 of them reported skin improvement(as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 50% of women over the age of 50? Test using a = 0.05. (a) Test statistic: z = (6) Critical Value: z* = (c) The final conclusion is A. There is not sufficient evidence to reject the null hypothesis that p = 0.5. That is, there is not sufficient evidence to reject that the crean can improve the skin of more than 50% of women over 50. B. We can reject the null hypothesis that p = 0.5 and accept that p > 0.5. That is, the cream can improve the skin of more than 50% of women over 50. (2 points) The sample mean and standard deviation from a random sample of 15 observations from a normal population were computed as * = 31 and s = 14. Calculate the t statistic of the test required to determine whether there is enough evidence to infer at the 9% significance level that the population mean is greater than 26. Test Statistic

Answer 1

Solution. Consider problem v Given, x 720 # n=1400 os143 co 11 120 1400 To test Ho', p=0.50 HP70.50 a) Test statistic : ZE P-Po Poll-P.) 0:5143-015 0.500.5) 1400 7.0 70359 Z= 0.0143 0.01336 1.07o Z - b) p-value - = RC271.070) -0.1423 Som etable P-value 0.1423 A Now, consider Problem and Given x=30 noso -- = 30 -0.6 50 d20:05 To test Hos POS # Pos rls q Test statistici za Po Pocl-P.) 0.6-OS 0.500:5)

z = ol 0.0707 z = 1.4 144 - Test statistic :z=1.414 b) critical value value = Zq = Zoos = 1.645 critical value = 1.645 z < Za we do not reject Ho at sit los. There is not sufficient evidence to ngect the null hypothesis that pzos, That is, there is not sufficient evidence to reject that the ream can improve the skin of more than sol. of women ovez so. concidez problem and Giren, x=31 14 n = 15 Q=0:0g we want to test Ho M=26 Hi 4726 s Test statistic صدای tă x-lo 31-26 191 is 5 21:3832 3.614 8 ta 1383 Test Statistic

P-value = 0.0941 bom t-table --p-value >0.09 (0) a. we do not reject to at gl. lois. er There is not that the than 26. population nough evidence to inter mean is greater