The Gidget Company makes widgets If the production process i

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 3.37 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 .05 level of significance. What decisions do you make using the critical value approach to hypothesis testing?

B. Null hypothesis: If you test the null hypothesis at the

0.01 level ofsignificance, what decision do you make using thep-value approach to hypothesistesting?

Recall from part (a) that the null and alternative hypotheses are as shown below, the sample size is

n=__,the level of significance is =0.01,and because is unknown, the t distribution and the

tSTAT test statistic must be used. Again, assume that the length of the widgets is normally distributed

Hence the null hypotheses will ___________be rejected.

c. Interpret the meaning of the p-value in this problem.

The p-value is the probability of getting a test statistic equal to or more extreme than the sample result, given that the null hypothesis, H0, ____. Use this information to interpret the p-value in this case.

d. Compare your conclusions in (a) and (b).

Examine the conclusions made in parts (a) and (b) above. If the conclusions to the hypothesis test differ among the two differentmethods, then consider any reasons for this occurrence. Similarly, if the conclusions to the hypothesis test are the same among the two differentmethods, then consider any reasons why this would be the case.

Solution

Set Up Hypothesis
Null, H0: U=3.4
Alternate, H1: U!=3.4
Test Statistic
Population Mean(U)=3.4
Sample X(Mean)=3.37
Standard Deviation(S.D)=0.24
Number (n)=25
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =3.37-3.4/(0.24/Sqrt(24))
to =-0.625
| to | =0.625
Critical Value
The Value of |t a| with n-1 = 24 d.f is 2.064
We got |to| =0.625 & | t a | =2.064
Make Decision
Hence Value of |to | < | t a | and Here we Do not Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != -0.625 ) = 0.5379
Hence Value of P0.05 < 0.5379,Here We Do not Reject Ho

a) If you test the null hypothesis at the .05 level of significance.
What decisions do you make using the critical value approach to hypothesis testing?

Null & Alternative are : H0: U=3.4, H1: U!=3.4
Critical Value: -2.064,2.064
test statistic: to =-0.625
and the decision is |to | < | t a | and Here we Do not Reject Ho

b) Null hypothesis: If you test the null hypothesis at the 0.01 level of?significance

Null & Alternative are : H0: U=3.4, H1: U!=3.4
Critical Value: -2.797,2.797
test statistic: to =-0.625
and the decision is |to | < | t a | and Here we Do not Reject Ho

c)
P-value = ( P != -0.625 ) = 0.5379

d)
conclusions to the hypothesis test are the same among the two different methods