Question

IQ scores follow a Normal distribution with a mean μ = 100 and standard deviation σ = 15. A SRS of 31 seventh-grade girls in one school district is tested and the sample mean x¯¯¯x¯ was = 102 . Is there evidence that the mean IQ score in this district is different from from 100?

The alternative hypothesis is:

Ha: u < 100

Ha: u > 100

Ha: u ≠ 100

The test statistic, z =....... (+ 0.01)

P(z ) =........ (+ 0.0001)

Conclusion:

Is this sufficient evidence at αα = 0.05, to conclude that the IQ of students in this school district is different from than 100?

no

yes

3.

Returning to the study on systolic blood pressure in executives aged 35 - 44, if for a sample mean of systolic blood pressure in a randomly selected sample of executives aged 35 - 44, following a a statistical test of the hypotheses Ho: μ=128μ=128 vs. Ha: μ≠128μ≠128, we reject Ho our conclusion is that the mean (μμ) systolic blood pressure for the population from which the sample was taken :

is not equal to 128

is equal to 128

.

If the true value of the population mean of systolic blood pressure in the population from which the sample was taken is 128, we have made a:

Correct decision

Type I error

Type II error

Answer 1

Question 1

To Test :-

H₀ :-  

H₁ :-  

Test Statistic :-

Test Criteria :-  

Reject null hypothesis if

Critical value

Result :- Fail to reject null hypothesis

Conclusion :- Accept Null Hypothesis

There is no evidence to support the claim that the IQ of students in this school district is different from than 100.

P value = P ( Z > 0.74 ) = 1 - P ( Z < 0.74 ) = 1 - 0.7711 = 0.2289

Multiplying the probability by 2, since the alternative hypothesis is two tailed ( two sided )

P - value = 2 * 0.2289 = 0.4578