Question

The operations manager of Slug Computers is considering a new method of assembling its Mollusk Computer. The present method requires 42.3 minutes, on average to assemble the speedy computer. The new method was introduced and a random sample of 24 computers revealed a mean assembly time of 40.6 minutes with a standard deviation of 2.7 minutes, the distribution is normal.

At the .10 level of significance, can we conclude the new method is faster, on average?

Estimate the p value.

So my problm with this question is how to calculate the P-value . I need the P- value part to be explained in detail please and thank you.

Answer 1

Let denotes the mean assembly time in the new method.

To test against

Here

sample mean

sample standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 10% level of significance if P-value < 0.1

Now,

The value of the test statistic

P-value

Using Mintab software, calc-> Probability distribution -> t -> cumulative distribution, we got the p-value

Since P-value = 0.0026179 < 0.1, so we reject H₀ at 10% level of significance and we can conclude that he new method is significantly faster, on average.