Answer: 8359
Step-by-step explanation:
The formula for sample size needed for interval estimate of population proportion :-
Given : The significance level :
Critical value :
Previous estimate of proportion :
Margin of error :
Now, the required sample size will be :-
Hence, the required sample size = 8359
Answer:
Since the p value is higher than the significance level given of 0.01 we don't have enough evidence to conclude that the true mean for group 1 is significantly higher thn the true mean for the group 2.
Step-by-step explanation:
Data given
represent the sample size for group 1
represent the sample size for group 2
represent the sample mean for the group 1
represent the sample mean for the group 2
represent the sample standard deviation for group 1
represent the sample standard deviation for group 2
System of hypothesis
The system of hypothesis on this case are:
Null hypothesis:
Alternative hypothesis:
We are assuming that the population variances for each group are the same
The statistic for this case is given by:
The pooled variance is:
We can find the pooled variance:
And the pooled deviation is:
The statistic is given by:
The degrees of freedom are given by:
The p value is given by:
Since the p value is higher than the significance level given of 0.01 we don't have enough evidence to conclude that the true mean for group 1 is significantly higher thn the true mean for the group 2.