Question

Use .05 level of significance

Find the P-Value-

Find the test statistic Zo-

three sixty two / (eleven hundred) successful

three ninety six / (eleven hundred) successful

Did proportion change? It just says one was 50 years ago the 362 and the next one was is today. thats all it says, theres no sd

Answer 1

When the population proportions are not known, the standard deviation of the sampling distribution can be calculated from the equation below by assuming that the sample size n₁ and n₂ to be less than 5% of the population size

S.E=0.0202

Test statistic ,

Since the first sample was taken fifty years ago the study of interest would be probabily H₁: p₁<p_2.

If the alternative is the above mentioned one then the test would be a one tailed test and the p value will be 0.063

Here p-value >0.05 so staistically there is no evidence from the sample regarding the change in proportion at 5% significance level

Suppose if its a two tailed interest that means the alternative hypothesis would be

Then the p-value is 0.126

Please see the difference in the selection of normal curves

Here also p value >0.05 so we stick to our null hypothesis that there is no difference in the proportion. This conclusion of no statistical significance in the proportion can be drawn at 5% level of significance