Question

A machine that puts corn flakes into boxes is adjusted to put an
average of 15.4 ounces into each box, with standard deviation of
0.22 ounce. If a random sample of 17 boxes gave a sample standard
deviation of 0.33 ounce, do these data support the claim that the
variance has increased and the machine needs to be brought back
into adjustment? (Use a 0.01 level of significance.) (i) Give the
value of the level of significance.

State the null and alternate hypotheses.

*H*_{0}: *σ*^{2} = 0.0484;
*H*_{1}: *σ*^{2} > 0.0484

*H*_{0}: *σ*^{2} = 0.0484;
*H*_{1}: *σ*^{2} <
0.0484

*H*_{0}: *σ*^{2} = 0.0484;
*H*_{1}: *σ*^{2} ≠ 0.0484

*H*_{0}: *σ*^{2} < 0.0484;
*H*_{1}: *σ*^{2} = 0.0484

(ii) Find the sample test statistic. (Round your answer to two
decimal places.)

(iii) Find or estimate the *P*-value of the sample test
statistic.

*P*-value > 0.100

0.050 < *P*-value <
0.100

0.025 < *P*-value < 0.050

0.010 < *P*-value < 0.025

0.005 < *P*-value < 0.010

*P*-value < 0.005

(iv) Conclude the test.

Since the *P*-value ≥ *α*, we fail to reject the
null hypothesis.

Since the *P*-value < *α*, we reject the null
hypothesis.

Since the *P*-value < *α*, we fail to reject
the null hypothesis.

Since the *P*-value ≥ *α*, we reject the null
hypothesis.

(v) Interpret the conclusion in the context of the
application.

At the 1% level of significance, there is sufficient evidence to
conclude that the variance has increased and the machine needs to
be adjusted.

At the 1% level of significance, there is insufficient evidence to conclude that the variance has increased and the machine needs to be adjusted.

Answer #1

given,

significance level,

Degree of freedom=17-1=16

Critical Value are given

Test staticstics

Decision making

There is enough evidence to support the calim. that standard the variance has increased and the machine needs to be brought back into adjustmen.

..........................

H0: σ2 = 0.0484; H1: σ2 > 0.0484

test statistics = 36

P-value < 0.005

Since the P-value < α, we reject the null hypothesis.

At the 1% level of significance, there is sufficient evidence to conclude that the variance has increased and the machine needs to be adjusted.

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