1.test wheter these samples represent populations that are different from the general population- sample of 10 with a mean of 44 and sample of 1 with a mean of 48.
2. The general population of individuals has a mean of 40 , a deviation of 6, and follows a normal curve. for each sample, carry out a z test using the five stephs hypothesis testing with a two-tailed test at the .05
To answer the question, we need to conduct a z-test to determine whether these samples represent populations that are different from the general population.
1. First, let's clarify the hypothesis we want to test:
Null hypothesis (H0): The samples represent populations that are not different from the general population.
Alternative hypothesis (Ha): The samples represent populations that are different from the general population.
2. Calculate the test statistic (z-score) for each sample:
For the first sample:
Sample size (n1) = 10
Sample mean (x1̅) = 44
Population mean (μ) = 40
Population standard deviation (σ) = 6
The formula to calculate the z-score is:
z = (x1̅ - μ) / (σ / √n1)
Substituting the values, we get:
z1 = (44 - 40) / (6 / √10)
For the second sample:
Sample size (n2) = 1
Sample mean (x2̅) = 48
Population mean (μ) = 40
Population standard deviation (σ) = 6
The formula to calculate the z-score is:
z = (x2̅ - μ) / (σ / √n2)
Substituting the values, we get:
z2 = (48 - 40) / (6 / √1)
3. Find the critical value for a two-tailed test at the significance level of 0.05 (α = 0.05).
The critical value is obtained from a standard normal distribution table. For a two-tailed test with α = 0.05, the critical z-value is approximately ±1.96 (since we want to capture the extreme ends of the distribution).
4. Compare the calculated z-scores to the critical value.
If the calculated z-score falls within the critical value range, we fail to reject the null hypothesis (H0) and conclude that the samples do not represent populations different from the general population. Otherwise, if the calculated z-score is outside the critical value range, we reject the null hypothesis (H0) and conclude that the samples represent populations different from the general population.
5. Interpret the results of the z-tests.
Using the comparison results from step 4, interpret whether the samples represent populations that are different from the general population.