Question

Do shoppers at the mall spend less money on average the day after Thanksgiving compared to the day after Christmas? The 52 randomly surveyed shoppers on the day after Thanksgiving spent an average of $132. Their standard deviation was $29. The 40 randomly surveyed shoppers on the day after Christmas spent an average of $142. Their standard deviation was $34. What can be concluded at the αα = 0.10 level of significance?

For this study, we should use Select an answer t-test for the difference between two independent population means t-test for the difference between two dependent population means z-test for the difference between two population proportions t-test for a population mean z-test for a population proportion

1. The null and alternative hypotheses would be:   
2.   

H0:H0:  Select an answer μ1 p1  Select an answer < = ≠ >  Select an answer p2 μ2  (please enter a decimal)   

H1:H1:  Select an answer μ1 p1  Select an answer < = ≠ >  Select an answer p2 μ2  (Please enter a decimal)

2. The test statistic ? z t  =  (please show your answer to 3 decimal places.)
3. The p-value =  (Please show your answer to 4 decimal places.)
4. The p-value is ? > ≤  αα
5. Based on this, we should Select an answer reject accept fail to reject  the null hypothesis.
6. Thus, the final conclusion is that ...
   • The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population mean amount of money that day after Thanksgiving shoppers spend is less than the population mean amount of money that day after Christmas shoppers spend.
   • The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the mean expenditure for the 52 day after Thanksgiving shoppers that were observed is less than the mean expenditure for the 40 day after Christmas shoppers that were observed.
   • The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population mean amount of money that day after Thanksgiving shoppers spend is less than the population mean amount of money that day after Christmas shoppers spend.
   • The results are statistically insignificant at αα = 0.10, so there is statistically significant evidence to conclude that the population mean amount of money that day after Thanksgiving shoppers spend is equal to the population mean amount of money that day after Christmas shoppers spend.

Answer 1

t-test for the difference between two independent population means

Ho:mu1=mu2

Ha;mu1<mu2

alpha=0.10

t=x1bar-x2bar/sqrt9s1^2/n1+s2^2/n2)

=(132-142)/sqrt(29^2/52+34^2/40)

= -1.489503

t=-1.490

df=n1=n2-2=52+40-2=90

p value is

=T.DIST(-1.489503,90,TRUE)

0.069925538

p=0.0702

p-value is ≤  α

Reject Ho

The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population mean amount of money that day after Thanksgiving shoppers spend is less than the population mean amount of money that day after Christmas shoppers spend.

t-test for the difference between two independent population means

Ho:mu1=mu2

Ha;mu1<mu2

t=-1.490

p=0.0702

p-value is ≤  α

The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population mean amount of money that day after Thanksgiving shoppers spend is less than the population mean amount of money that day after Christmas shoppers spend.