Answer:
The success rate for the full campaign will be different than the standard rate of 2%.
Step-by-step explanation:
To predict the results conduct a hypothesis test for single proportion.
Assume that the significance level of the test is .
- The hypothesis is defined as follows:
The the success rate for the full campaign will be no different than the standard rate, i.e. <em>p</em> = 0.02
The the success rate for the full campaign will be different than the standard rate, i.e. <em>p</em> ≠ 0.02
- According to the Central limit theorem as the sample size is large, i.e, <em>n</em> = 50,000 > 30, the sampling distribution of sample proportion is normally distributed with mean and standard deviation. Then the test statistic is defined as:
Compute the value of the test statistic as follows:
The hypothesis test is two tailed. Then the for 5% level of significance the rejection region is defined as: , i.e if the test statistic value lies out of this region then the null hypothesis will be rejected.
The calculated value of the test statistic is <em>z</em> = 6.39.
That is, .
Thus, we may reject the null hypothesis.
As the null hypothesis is rejected at 5% level of significance this implies that the success rate for the full campaign will be different than the standard rate of 2%.