## 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.

#### MANOVA, 5. Perform a factorial MANOVA on the data. Before interpreting the ...

5. Perform a factorial MANOVA on the data. Before interpreting the multivariate results of the MANOVA, check outcomes that test other assumptions for this statistic: equality of co

#### Average Speed in Various Cases, Define Average Speed in Various Cases (a) ...

Define Average Speed in Various Cases (a) Particles covering different distances in different times say a particle covers s1 distance in time t1 ,s2 in time t2, s3 in time t3 and

#### Calculate its stationary probabilities, A small specialized workshop is use...

A small specialized workshop is used to perform periodic check-up on some high-tech devices. The check up is made in three stages whose durations are independent random variables w

#### Bank Reconciliation, need to understand bank recon...

need to understand bank recon...

ggg

#### Estimate the population mean flying time for the pilots, The mean number of...

The mean number of hours of flying time for pilots at Continental Airlines is 49 hours per month (The Wall Street Journal, February 25, 2003). Assume that this mean was based on ac

#### Jovian moons more geologically active than rocky planet, Why are Jovian moo...

Why are Jovian moons more geologically active than small rocky planets? - Ices deform and melt at much lower temperatures than rock, allowing icy volcanism and tectonics at sur

#### Probability, Mike sells on the average 15 newspapers per week (Monday – Fri...

Mike sells on the average 15 newspapers per week (Monday – Friday). Find the probability that 2.1 In a given week he will sell all the newspapers

#### Retained earnings , need help finding my retianed earnigns

need help finding my retianed earnigns

#### depreciation during the financial year, Depreciation during the financial ...

Depreciation during the financial year  The Resources which are bought during the economical season and its determined that the Depreciation will be incurred on them @ 10% PA it  