Question

November 6, 2012 was election day. Many of the major television networks aired coverage of the incoming election results during the primetime hours. For a random sample of 25 U.S. adults, the average time spent watching election coverage was 80.44 minutes with standard deviation of 43.99 minutes. We want to do a hypothesis test to see if this is sufficient evidence to reject the null hypothesis in favor of the alternative:

H₀: the mean number of minutes watching election coverage is <= 75 minutes

Ha: the mean number of minutes watching election coverage is > 75 minutes

a) Calculate the t test statistic for this test.

B) Assume that the p-value is .271. Is this set of data sufficient to reject the null hypothesis?  

a) No, p-value is not < .1

b) Yes, p-value is > .1

Answer 1

Answer

(A) Given that x(bar)= 80.44, standard deviation s = 43.99, sample size is n = 25 and population mean (mu) = 75

test statistics t=

$(\bar{x}-\mu)/(s/\sqrt{n}) \\ = (80.44-75)/(43.99/\sqrt{25}) \\ = 5.44/8.798 \\ = 0.618$

(B) Given that p value is 0.271, it is clear that this is more than 0.1. So, we failed to reject the null hypothesis as p value is greater than alpha level.

option (a) is correct