3. A developer wants to know if the houses in two different neighborhoods were built at roughly the same time. She takes a random sample of six houses from each neighborhood and finds their ages from local records. The accompanying table shows the data for each sample (in years). Assume that the data come from a distribution that is Normally distributed. Use data: Neighborhood 1 Neighborhood 2 58 33 63 42 54 32 55 37 48 51 52 57 a. Test the null hypothesis at a = 0.05 using the pooled t-test. Write null and alternative hypotheses. b. Find t-test c. Find p-value d. State your conclusion. e. Find 95% confidence interval and interpret2. A supermarket chain wants to know if their "buy one, get one free" campaign increases customer traffic enough to justify the cost of the program. For each of 10 stores they select two days at random to run the test. For one of those days (selected by a coin flip), the program will be in effect. They want to test the hypothesis that there is no mean difference in traffic against the alternative that the program increases the mean traffic. The accompanying table shows the number of customer visits to each of the 10 stores. Complete parts a through i below. Use data: With Program Without Program 151 143 222 221 127 116 47 44 332 333 141 138 121 121 28 37 190 176 14 149 a) Are the data paired? b) Find the mean difference. That is, the mean of the pairwise differences (With Program minus Without Program). c) Compute the standard deviation of the differences. d) Compute the standard error of the mean difference. e) Find the value of the t-statistic. f) Find the degrees of freedom. g) Is the alternative one or two sided? h) Find the p-value? i) At alpha=0.05, what do you conclude