Question

1. At store A, the sample average amount spent by a random sample of 32 customers was $31.22 with a sample standard deviation of $6.48. At store B, the sample average amount spent by a random sample of 36 customers was $34.68 with a sample standard deviation of $5.15. Test, using the 4-step procedure and a 5% level of significance, whether or not there is a difference between the population mean amount spent per customer at store A and the population mean amount spent per customer at store B.

2.

The Gallup organization conducts extensive annual studies of American adults. For their 2016 study, they analyzed survey results for a random sample of 750 American adults. They found that 56.8% of the adults sampled have at least 1 credit card. a. Determine a 98% confidence interval estimate for the population proportion of all American adults who have at least 1 credit card. b. Give a complete confidence statement. c. Determine whether the conditions required for this confidence interval are satisfied

Answer 1

n1 = 32

= 31.22

s1 = 6.48

n2 = 36

= 34.68

s2 = 5.15

Claim: There is a difference between the population mean amount spent per customer at store A and the population mean amount spent per customer at store B.

The null and alternative hypothesis is

For doing this test first we have to check the two groups have population variances are equal or not.

The null and alternative hypothesis is

Test statistic is

F = largest sample variance / Smallest sample variances

F = 41.9904 / 26.5225 = 1.58

Degrees of freedom => n1 - 1 , n2 - 1 => 32 - 1 , 36 - 1 => 31 , 35

Critical value = 1.779 ( Using f table)

Critical value > test statistic so we fail to reject null hypothesis.

Conclusion: The population variances are equal.

So we have to use here pooled variance.

Test statistic is

Degrees of freedom = n1 + n2 - 2 = 32 + 36 - 2 = 66

Critical value = 1.997 ( Using t table)

| t | > critical value we reject null hypothesis.

Conclusion: There is a difference between the population mean amount spent per customer at store A and the population mean amount spent per customer at store B.