Question

A machine is set to produce disc plates with a mean diameter of 14 mm. A sample of 8 discs gave a mean diameter,

x=14.9 mm and a standard deviation, s=1.33 mm. A test was carried out at the 5% level of significance to determine whether the machine is in good working order. Assume that the diameter of the disc follows a normal distribution.
i. State, in symbols, the null and alternate hypotheses for this test.

Answer 1

The null hypothesis states the mean diameter of the disc plates produced by the machine is 14 mm, while the alternate hypothesis states the mean diameter is different from 14 mm. A hypothesis test with a significance level of 5% is used to test the hypotheses.

Step-by-step explanation:

The null and alternate hypotheses for this test can be stated as follows:

Null Hypothesis (H0): The mean diameter of the disc plates produced by the machine is 14 mm.

Alternate Hypothesis (H1): The mean diameter of the disc plates produced by the machine is not equal to 14 mm.

To test these hypotheses, we use a hypothesis test with a significance level of 5% (0.05).

We calculate the test statistic, which is the t-score:

t = (x - μ) / (s / √n)

In this case, x=14.9 mm, μ=14 mm, s=1.33 mm, and n=8 (sample size).

After calculating the t-score, we compare it to the critical t-value at a significance level of 5% and degrees of freedom (n-1).

If the t-score falls in the rejection region (outside the critical t-value range), we reject the null hypothesis and conclude that the machine is not in good working order.

Based on the test results and the calculated t-score, we can draw a conclusion about the machine's performance.