Question

The Gidget Company makes widgets. If the production process is working​ properly, it turns out that the widgets are normally distributed with a mean length of at least 3.4 feet. Larger widgets can be used or altered but shorter widgets must be scrapped. You select a sample of 25 ​widgets, and the mean length is 3.35 feet and the sample standard deviation is 0.24 foot. Do you need to adjust the production​ equipment? Complete parts​ (a) through​ (d). If you test the null hypothesis at the 0.01 level of​ significance, what decision do you make using the critical value approach to hypothesis​ testing? what is the tstatistic critical value p value

Answer 1

H0: >= 3.4

Ha: < 3.4

Test statistics

t = ( - ) / ( S / sqrt(n) )

= ( 3.35 - 3.4) / (0.24 / sqrt(25) )

= -1.04

This is test statistics value.

df = n - 1 = 25 - 1 = 24.

t critical value at 0.01 significance level with 24 df = -2.49

From T table,

p-value with test statistics of 1.04 and df of 24 = 0.1544

That is with 24 df , P(T < -1.04) = 0.1544

Since p-value > 0.01 , we fail to reject null hypothesis.

We conclude at 0.01 significance level that we fail to support the claim.