help! where do i begin with this problem...in one area, monthly incomes of technology related workers have a standard deviation of $650. It is believed that the standard deviation of monthly incomes of non-technology workers is higher. A sample of 71 non technology workers are randomly selected and found to have a standard deviation of $950. Test the claim that non-technology workers have a higher standard deviation. Use a= 0.05
I know we are testing H: mean = 950 and looking to prove that it is greater than. alpha is 0.05
To test the claim that non-technology workers have a higher standard deviation, we can use a hypothesis test. The null hypothesis (H0) will be that the non-technology workers' standard deviation is equal to or less than $650, and the alternative hypothesis (Ha) will be that the non-technology workers' standard deviation is greater than $650.
H0: σ ≤ $650 (Claim that non-technology workers' standard deviation is less than or equal to $650)
Ha: σ > $650 (Claim that non-technology workers' standard deviation is greater than $650)
To conduct this hypothesis test, we will use the F-test statistic, which is calculated by dividing the sample variances and comparing them to the theoretical F-distribution.
The formula for the F-test statistic is:
F = (s1^2) / (s2^2)
Where s1^2 is the sample variance of non-technology workers and s2^2 is the known population variance of technology workers.
Given that the sample of 71 non-technology workers has a sample standard deviation (s) of $950 and the known population standard deviation (σ) of technology workers is $650, we can calculate the F-test statistic:
F = (s1^2) / (s2^2)
F = (950^2) / (650^2)
F = 902,500 / 422,500
F ≈ 2.1343
Once the F-test statistic is calculated, we can compare it to the critical value from the F-distribution table to determine if we reject or fail to reject the null hypothesis.
To determine the critical value, we need to look at the degrees of freedom (df1 and df2). For this test, df1 is the sample size of the non-technology workers minus 1 (df1 = 71 - 1 = 70), and df2 is the sample size of the technology workers minus 1 (df2 = 1).
Using an alpha level of 0.05, we find the critical value from the F-distribution table for df1 = 70 and df2 = 1 is approximately 3.966.
Since the calculated F-test statistic of 2.1343 is less than the critical value of 3.966, we do not have enough evidence to reject the null hypothesis. This means we do not have enough evidence to support the claim that non-technology workers have a higher standard deviation.
In conclusion, based on the given information and the hypothesis test, we fail to reject the claim that non-technology workers have a standard deviation equal to or less than $650.