Question

Watate Website 2 A market analyst wants to know if the new website he designed is showing increased pace views per visit and call the summary statistics in the table to the right. You may assume that the data come from a dsbution that is Normal distributed Complete parts a through d below. S =24 a) Find a 95% confidence interval for the moon difference - pageviews from the two woboites (Round to two decimal places as needed) by Why is the confidence interval narrower than the one, { -3.064.261, based off of 5 randomly sampled customers for each website? Choose the correct answer below. O A The sample sizes are larger OB. The number of page views are significantly different in the sample OC. The contidence interval found in part als actualy wider than this interval Click to select your answer(s)

Answer 1

where 2212 Let M2, 62 gi ~ N(His o N(H2 ý -ý NI ng 2 2 ☺ Mi-M2, (7,-72) - (M.-H2) N(0,1) T Z = 2 + 12 respectively. But there are unknown and it is estimated by sids (a) Note that the 100 (1-2) of confidence interval for (Mi-M₂) can be written as ! Si' (J, Jz) + 22/2 S2 + ( ý, -92) - Z2/2 2 81 12 ชา . + > mi n. is the value of z such that o た P(Z <=242 ) = 7,32/2) P(z> 2 d/ ho - 22/2 22/2

It is given that n2=95 n = 90 y, 6.3 Y 2 = 6:2 52= 2.5 si = 2.4 Also 100(1-4)% = 95% 7 2 = 0.05 all By standard normal table, 24/2 = 1.96 Putting the values in the formula of confidence internal internal we get (6-3-6-2) - 1.96 (2-4)2 (6.3-6-2) +1.94 /(2.4)+(2.5) (2:5)? + 1 90 IS go 95 = (-0.61, 0.81) mean Thus, the 95% confidence interval for the difference, M, M2 will be (-0.61, 0-81)

(b) No to that, more narrow confidence interval more accurate. The more accuracy can be achieve by increasing the sample size that is why the confidence obtained in part (a) is narrower than 1-3-86, 4.26 Thus, the comect answer will be (A) The sample sizes are larger. (C) Since obtained confidence interval is (-0-61,81 soi Yes), o within the confidence interral. (d) The confidence interval suggest about the null hypothesis that the mean difference is o It suggests that one should fail to reject Hos since o is a plausible value for the true mean difference