Question

Do convenience stores charge a high price for convenience Specifically are the prices idher than a large box store, such as Walmart? You decide to investigate this question by gathering data on on the prices of 10 goods from a convenience store and from Walmart. You enter the data in the following spreadsheet: be the population Let me be the population mean price of a good at the convenience store, and mean price of a good at Walmart. What are the appropriate hypotheses? H and HP P HHH Hp Sand HR > • HP> and H SP Question 18 What is the most appropriate test for your hypotheses? Two sample test assuming equal variances Ftest for equality of variances Paired two sample t-test Two sample test assuming unequal variances Question 19 Run the appropriate test, with a 10. What is your p-value? Round to two decimal places. Question 20 What do you conclude? tot the age prices connectors were Re s ep > There is sufficient de than the average prices at Walmart convenience stores Do notre sincep > There is sufficient evidence that the average prices we greater than the average prices at Walmart. Do no t sincepa . There is insuficient evidence that the average prices at convenience stores wepeater than the average prices at Walmart. Reject sincep<0. There is sufficient evidence that the average prices at convenience wores we greater than the average prices at Walmart

Answer 1

Answer: Let mu1 and mu2 be the population means of Convenience and Walmart stores. The correct hypotheses for the given problem are-- H0: mu1 = mu2 vs Ha: mu1 > mu2.

We choose "Two-sample t-test assuming unequal variance" as the appropriate test for this case. In the given problem the test statistic is T=(x1bar-x2bar)/sqrt((s1*s1/n1)+(s2*s2/n2)) where x1bar, x2bar are the sample means; s1,s2 are the sample standard deviations and n1,n2 are the sample sizes. We reject H0 when T(observed) > t(alpha,v) where t(alpha,v) is the upper alpha point of a t-distribution with 'v' degrees of freedom. v = ((s1/n1)+(s2/n2))²/(((s1/n1)²)/(n1-1))+(((s2/n2)²)/(n2-1)) and alpha is the level of significance.

or if the p-value for the obtained test statistic is less than the level of significance.

The value of the observed test statistic is T = 0.0607, t(alpha,v) = 1.3306

We see that T(observed) < t(alpha,v)

Here, the p-value for the observed test statistic is = 0.48 (rounded to 2 decimals)

Here, p > alpha. So we do not reject H0 and conclude on the basis of the given sample that the average price of the convenience stores is not greater than that of Walmart stores.

[The answers are obtained using R-software. Codes and Output are attached below].

RR Console > xl=c(3.3,1.29,2.27,3.17,1.94,6.54, 13.05, 18.43,0.76,9.57) > x2=C (2.61,1.94,1.6,1.97, 4.88, 4.99,9.94,17.14,1.44, 13.36) > xlbar=mean (xl) x2bar=mean (x2) > nl-length (xl) > n2=length (x2) 31=var (x2) > 32=var (x2) V / > =ixiba:-z2bar)/sqrt((s./nl) + (92/n2) | [1] 0.06070274 > Yriisi/nl) + ($2/02) 149 > vo= ( ( (s171)2)/(1-11) -1 (32/2)^2) / 162-1)). v=vn/vd (1) 1.330607 (11 0.4761339 LA