Question

In: Statistics and Probability

In the past, Dumont Clothing Store had 72% charge purchases and 28% cash purchases. A representative...

In the past, Dumont Clothing Store had 72% charge purchases and 28% cash purchases. A representative sample of 200 recent purchases shows that 160 were charge purchases. Does this suggest a statistically significant change in the paying practices of Dumont customers?

1-Hypothesis test for one population mean (unknown population standard deviation)

2-Confidence interval estimate for one population mean (unknown population standard deviation)

3-Hypothesis test for population mean from paired differences

4-Confidence interval estimate for population mean from paired differences

5-Hypothesis test for difference in population means from two independent samples

6-Confidence interval estimate for difference in population means from two independent samples

7-Hypothesis test for one population proportion

8-Confidence interval estimate for one population proportion

9-Hypothesis test for difference between two population proportions

10-Confidence interval estimate for difference between two population proportions

Solutions

Expert Solution

7-Hypothesis test for one population proportion

(bellow is test details):

null Hypothesis:               Ho:   p = 0.720
alternate Hypothesis:    Ha: p 0.720
for 0.05 level with two tailed test , critical z= 1.9600
Decision rule :   reject Ho if absolute value of test statistic |z|>1.96
sample success x   = 160
sample size          n    = 200
std error   se =√(p*(1-p)/n) = 0.0317
sample proportion p̂ = x/n= 0.8000
test stat z =(p̂-p)/√(p(1-p)/n)= 2.52
since test statistic falls in rejection region we reject null hypothesis
we have sufficient evidence to conclude that,there is a statistically significant change in the paying practices of Dumont customers

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