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The Gidget Company makes widgets. If the production process is working properly,

ID: 3268289 • Letter: T

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 3.3 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 3.23 feet and the sample standard deviation is 0.24 foot. Do you need to adjust the production equipment? Complete parts (a) through (d). Click here to view page 1 of the critical values for the t Distribution. Click here to view page 2 of the critical values for the t Distribution. a. If you test the null hypothesis at the 0.05 level of significance, what decision do you make using the critical value approach to hypothesis testing? What are the null and alternative hypotheses for this test? A. H_0: mu greaterthanorequalto 3.3 H_1: mu 3.3 What is the test statistic for this test? (Round to four decimal places as needed.) What is the critical value for this test? (Round to four decimal places as needed.)

Explanation / Answer

The statistical software output for this problem is:

One sample T summary hypothesis test:
: Mean of population
H0 : = 3.3
HA : < 3.3

Hypothesis test results:

Hence,

a) Hypotheses: Option A is correct.

Test statistic = -1.4583

Critical value = -1.7109

Mean Sample Mean Std. Err. DF T-Stat P-value 3.23 0.048 24 -1.4583333 0.0789
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