If Ho: μ = 50 and Ha: mu. = 59 and s = 10 what is αlpha if x exceeds 56for n=25
Do you mean 59 or 56?
Z = (score-mean)/SD
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n = 10/√25 = ?
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
To find the value of α (alpha), we first need to determine the critical region for the hypothesis test. Given that the null hypothesis (Ho) is μ = 50 and the alternative hypothesis (Ha) is μ > 59, we are conducting a one-tailed upper-tailed test.
Next, we calculate the test statistic (z) using the formula:
z = (x - μ) / (s / √n)
Here, x is the sample mean, μ is the population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size.
In this case, x exceeds 56, so x = 56. The population mean under the null hypothesis is μ = 50, the sample standard deviation is s = 10, and the sample size is n = 25.
Substituting these values into the formula:
z = (56 - 50) / (10 / √25)
z = 6 / (10 / 5)
z = 6 / 2
z = 3
Now, we can look up the critical value of the z-test using a standard normal distribution table or calculator. The critical value will correspond to the significance level α.
Assuming a significance level of α = 0.05 (5%), the critical value for a one-tailed upper-tailed test is approximately 1.645.
Since the calculated test statistic (z = 3) is greater than the critical value (1.645), we reject the null hypothesis in favor of the alternative hypothesis.
Therefore, the value of α (alpha) is equal to the chosen significance level of 0.05, indicating a 95% confidence level.