Question

Marketers at PaperClips a regional office supply chain, are researching whether the population mean amount spent on back to -school shopping for students in grades K-12 has changed from 2016 to 2018, Based on market research the marketers assume that the population standard devation is $101.52 for 2016 and $96.47 for 2018, Households across the region with at least one student in grades K-12 were randomly selected in 2016 and again in 2018. The results are shown in the table below. Explain whether a hypothesis test for the difference between two means of independent samples ins appropriate, and if so, find the null and alternative hypotheses, where μ, s the population mean amount spent on back-t school shopping per household in 2016 and pu is the population mean amount spent on back-to-school shopping per household in 2018 2016 $521.54 534 2018 1$496.92 n2511 Select the correct answer below O All of the conditions to conduct the hypothesis test are met The null and test are met. The null and alternative hypotheses are O All of the conditions to conduct the hypothesis test have been met. The nultland alternative hypotheses are O All of the conditions to conduct the hypothesis test are met. The null and a alternative hypotheses are O Although the samples are randomly selected, independent and sufficiently large. the population standard deviation is not known for both years O Although the population standard deviations are known and the sample sizes are sufficiently large, the samples are not randomly selected and are not independent of each other. O Although the population standard deviations are known and the samples are randomly selected and independent, the sample sizes are not sufficiently large.

Answer 1

H0 : mu1 - mu2 = 0
HA: mu1 -mu2 not equals to 0

test statistics:

z = (x1 -x2)/sqrt(s1^2/n1+s2^2/n2)
= ( 521.54 - 496. 92)/sqrt(101.52^2/534 + 96.47^2/511)
= 4.020

p value = 0.00005

Reject H0 at 0.05 alpha