Question

Screws Inc. has asked for assistance in determining whether the manufacturing process is operating correctly. When the process is operating properly, it produces screws whose weights are normally distributed with a population mean of 5 grams and a population standard deviation of 0.1 grams.The manager wishes to know if the recent change to a new materials supplier has lowered the weight of the screws. In a random sample of 16 screws, the sample mean weight is 4.962 grams. Is there evidence to conclude that lower weight screws are now being produced at a significance level of 5%? O A. The p-value is 0.0643, and we reject the null hypothesis. O B. The p-value is 0.0643, and we fail to reject the null hypothesis. C. The p-value is 0.1286, and we accept the alternative hypothesis that ,yes, the screws appear to have a lower weight D. The p-value is 0.1286, and we fail to reject the null hypothesis.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 5

H_a : $\mu$ < 5

$\bar x$ = 4.962

$\mu$ = 5

$\sigma$ = 0.1

n = 16

Test statistic = z

= ($\bar x$ - $\mu$) / $\sigma$ / $\sqrt$n

= (4.962 - 5) / 0.1 / $\sqrt$16

= -1.52

Test statistic = -1.52

This is the right tailed test .

P(z <-1.52) = 0.0643

P-value = 0.0643

$\alpha$ = 5% = 0.05

P-value > $\alpha$ .  Fail to reject the null hypothesis .

B)