In: Statistics and Probability
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
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 |