The mean annual incomes of certified welders are normally distributed with the mean of $50,000 and a population standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. A sample of 100 welders is taken and the mean annual income of the sample is $50,350. If the level of significance is 0.10, what conclusion should be drawn?A. Do not reject the null hypothesis as the test statistic is less than the critical value of z. B. Do not reject the null hypothesis as the test statistic is less than the critical value of t. C. Reject the null hypothesis as the test statistic is greater than the critical value of t. D. Reject the null hypothesis as the test statistic is greater than the critical value of z.
Accepted Solution
A:
Answer:Their welders earn $50,000 annually.Step-by-step explanation:Given : [tex]\mu = 50,000[/tex] [tex]\sigma = 2000[/tex] n = 100 [tex]\bar{x}=50350[/tex]To Find : The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. Solution :[tex]H_0:\mu = 50000\\H_a: \mu \neq 50000[/tex]n = 100 Since n > 30So we will use z test[tex]z= \frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]Substitute the values [tex]z= \frac{50350-50000}{\frac{2000}{\sqrt{100}}}[/tex][tex]z=1.75[/tex]Refer the z table for p value p value = 0.9599α= 0.05Since p value > αSo we accept the null hypothesis .Hence their welders earn $50,000 annually.