Answer:
a) Null hypothesis:
Alternative hypothesis:
b)
c)
d) If we compare the p value and the significance level given we see that so we can conclude that we have enough evidence to reject the null hypothesis, and the more experience consultant A have a significant higher rate compared to the consultant B with less experience at 5% of significance.
Step-by-step explanation:
1) Data given and notation
represent the mean for the sample of Consultant A
represent the mean for the sample of Consultant B
represent the sample standard deviation for the sample of Consultant A
represent the sample standard deviation for the sample of bonsultant B
sample size selected for the Consultant A
sample size selected for the Consultant B
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
Part a: State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean for the Consultant A (more experience) is higher than the mean for the Consultant B, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".
Part b: Calculate the statistic
We can replace in formula (1) the info given like this:
Part c: P-value
The first step is calculate the degrees of freedom, on this case:
Since is a one side test the p value would be:
Part d: Conclusion
If we compare the p value and the significance level given we see that so we can conclude that we have enough evidence to reject the null hypothesis, and the more experience consultant A have a significant higher rate compared to the consultant B with less experience at 5% of significance.