0.32 Ps 0.30 N 322. 2 a. SOC The students at Regional High School cut an average

Question

0.32 Ps 0.30 N 322. 2 a. SOC The students at Regional High School cut an average of 3.3 classes per month. A random sample of 117 seniors averages 3.8 cuts per month, with a standard deviation of 0.53. Are seniors significantly different from the student body as a whole? (HINT: The wording of the research question suggests a two-tailed test. This means that the alternative, or research, hypothesis in step 2 will be stated as HI: Au 3.3 and that the critical region will be split between the upper and lower tails of the sampling distri- bution. See Table 8.3 for values of Z(critical for various alpha levels.

Explanation / Answer

8.2)

Part a:

Null and Alternative Hypothesis:

H0: µ = 3.3

H1: µ 3.3

Level of significance:

a = .05

Test Statistics:

z = ( x bar - µ) / (s/Ön)

= (3.8 -3.3)/(0.53/Ö117)

= 10.2

Decision:

From normal table at 5% level of significance we get the critical value as -1.96 and +1.96.

Here the test statistics is greater than 1.96, so it falls in rejection region. We reject the null hypothesis.

Conclusion:

There is sufficient evidence to conclude that seniors are significantly different from the student’s body as a whole.

Part b:

Null and Alternative Hypothesis:

H0: µ = 3.3

H1: µ > 3.3

Level of significance:

a = .05

Test Statistics:

z = ( x bar - µ) / (s/Ön)

= (3.8 -3.3)/(0.53/Ö117)

= 10.2

Decision:

From normal table at 5% level of significance we get the critical value as 1.645

Here the test statistics is greater than 1.645, so it falls in rejection region. We reject the null hypothesis.

Conclusion:

There is sufficient evidence to conclude that seniors are significantly greater from the student’s body as a whole.

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