## Identification of null and alternative hypotheses, Basic Statistics

Assignment Help:

A politician claims that the mean salary for managers in his state is more than national mean \$82,000.  The salaries (in dollars) for a random sample of 30 managers in the state are listed. At α = 0.07, is there enough evidence to support the claim?

 86,809 72290 81862 79764 79511 75716 72039 83358 90425 95658 85221 72387 85468 76680 76529 98304 97118 74618 90788 83777 99303 92608 79489 72045 79296 90872 72865 82948 84042 93539

Solution:

a) Identification of Null and alternative hypotheses:

Null hypothesis:

H0 The mean salary for managers in the state is not more than \$82000

H0  µ ≤ 82000

alternative hypothesis:

H0  The mean salary for managers in the state is more than \$82000

H0  µ > 82000

Level of significance (α) = 0.07                         One tailed test

Assumptions:

Population is normally distributed.

Data Information: In the above data we find

n (Sample size) =  30

σ (Population standard deviation)   = 8315.90

X‾ (Sample mean) = 83410.97

b) Calculation of Test Statistic:

c) Finding P value

P value   = P (Z > Z observed)

= P (Z > 0.93)

= 1 - P(Z < 0.93)

= 1- 0.8238

= 0.1762

d) Decision Rule:

Reject H0 if P value is less than the level of significance.

Decision:

Since P value (observed level of significance) = 0.1762 is greater than α (level of significance) = 0.07, we fail to reject H0.

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