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Answer:
a. Null hypothesis:
Alternative hypothesis:
b.
c.
So with the p value obtained and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (Low Blood Lead level) is significantly higher than the mean for the group 2 (High Blood Lead level).
Step-by-step explanation:
a. State and label the null and alternative hypotheses.
The system of hypothesis on this case are:
Null hypothesis:
Alternative hypothesis:
Or equivalently:
Null hypothesis:
Alternative hypothesis:
Our notation on this case :
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
b. State the value of the test statistic.
And the statistic is given by this formula:
Where t follows a t distribution with degrees of freedom. If we replace the values given we have:
Now we can calculate the degrees of freedom given by:
c. Find either the critical value(s) and draw a picture of the critical region(s) or find the P-value for this test. Indicate which method you are using: ( CIRCLE ONE: Critical value / P-value )
Method used: P value
And now we can calculate the p value using the altenative hypothesis, since it's a right tail test the p value is given by:
So with the p value obtained and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (Low Blood Lead level) is significantly higher than the mean for the group 2 (High Blood Lead level).