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.

Posted Date: 3/16/2013 3:09:55 AM | Location : United States

Ask an Expert

Related Discussions:- Identification of null and alternative hypotheses, Assignment Help, Ask Question on Identification of null and alternative hypotheses, Get Answer, Expert's Help, Identification of null and alternative hypotheses Discussions

Write discussion on Identification of null and alternative hypotheses
Your posts are moderated

Write your message here..

Related Questions

Proton-neutron hypothesis, This hypothesis was put forward by Heinsberg aft... This hypothesis was put forward by Heinsberg after the discovery by Chadwick. According to this hypothesis, a nucleus of mass number A and atomic number Z contains Z protons, and

The data analysis process and statistical techniques, I need to conduct an... I need to conduct an analysis' on an alcohol and substance abuse study. the data set is too large to upload . The data set is the SPSS version that I need to work from. Here is the

Calculate permanent income, Suppose that permanent income, YP (t) is calcu... Suppose that permanent income, YP (t) is calculated as the average of disposable income (YD t ) over the past 5 years, that is: YP (t) = 0.2(YD t + YD t-1 + YD t-2 + YD t-3

Profit and loss accounting, what does it mean by sales less of goods sold a... what does it mean by sales less of goods sold and cost less of goods sold

Ex. 3-12, EXERCISE 3-12 Computing Predetermined Overhead Rates and Job Cos... EXERCISE 3-12 Computing Predetermined Overhead Rates and Job Costs [LO1,LO2, LO3, LO7] Kody Corporation uses a job-order costing system with a plantwide overhead rate based on ma

Calculate the p-value for the test statistic value, A subject is asked to p... A subject is asked to pick the suit of a card that she does not see, picked at random from a standard deck of playing cards. If the subject has no extra-sensory powers (ESO) her gu

How will the adoption of ifrs change financial reporting, How will the adop... How will the adoption of IFRS change financial reporting by companies? Manager 1: The new rules will definitely change the way our organization prepares financial statements.

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

Frequency distribution, hey goo day, i wanna know the definition of frequen... hey goo day, i wanna know the definition of frequency distribution and how to conduct it like in examples?

Karl Pearsons, ). Calculate Karl Pearson’s coefficient of correlation from... ). Calculate Karl Pearson’s coefficient of correlation from the following data , using 20 as the working mean for price and 70 as the working mean for demand: Price: 14 16 17 18 1