Respuesta :
Answer:
The standard deviation used to calculate the test statistic for the one-sample z-test is 0.04.
Step-by-step explanation:
A single proportion z-test can be performed to determine whether the proportion of people in Norway with a blood type of A positive is different from that in the United States.
It is provided that the percentage of people in the US with blood type A positive is, p = 36%.
A random sample of n = 150 people from Norway are selected to check the above claim.
The hypothesis can be defined as:
H₀: The proportion of people in Norway with a blood type of A positive is same as that in the United States, i.e. p = 0.36.
Hₐ: The proportion of people in Norway with a blood type of A positive is different from that in the United States, i.e. p ≠ 0.36.
The test statistic for the the hypothesis testing is:
[tex]z=\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}[/tex]
The mean of the sample proportion is:
[tex]\mu_{\hat p}=p[/tex]
The standard deviation of sample proportion is:
[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]
Compute the standard deviation value as follows:
[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]
[tex]=\sqrt{\frac{0.36(1-0.36)}{150}}[/tex]
[tex]=0.03919184\\\approx0.04[/tex]
Thus, the standard deviation used to calculate the test statistic for the one-sample z-test is 0.04.
