Question

This is the same data as the previous question. Suppose that you collected data on the grades at a local middle school and you wanted to know if males were more likely to fail than females. Using the data shown below, which of the following conclusions would be a correct conclusion from this study, if we used an alpha of .05? Round your answer to the nearest 2 decimal places. Pass Fail Males 100 27 Females 80 70 a. We would fail to reject the null hypothesis b. We would reject the null hypothesis c. We do not have enough information d. We would neither reject nor fail to reject the null hypothesisl

Answer 1

Here, we are doing the test for the difference in 2 proportions. The proportions being the fail rate of males vs fail rate for females.

The sample proportion here are computed as:

p₁ = 27/(100 + 27) = 0.2126
p₂ = 70/(70 + 80) = 0.4667

The pooled proportion here is computed as:

The standard error here is computed as:

The test statistic now is computed here as:

As this is a one tailed test, upper tailed test, the critical value for 5% level of significance here is given as:

P(Z > 1.645) = 0.05

As -4.42 < 1.645, therefore the test is not significant and a. We would fail to reject the null hypothesis