Identification of null and alternative hypotheses, Basic Statistics

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:

 403_distributed value.png

c) Finding P value

  179_finding p value.png

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







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
Related Questions
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

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

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

what does it mean by sales less of goods sold and cost less of goods sold

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

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 by companies? Manager 1: The new rules will definitely change the way our organization prepares financial statements.

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

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

). 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