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
H0: >= 3.4
Ha: < 3.4
t = ( - ) / ( S / sqrt(n) )
= ( 3.35 - 3.4) / (0.24 / sqrt(25) )
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.
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