USA today reported that the population mean life span of people who live in Hawa

Question

USA today reported that the population mean life span of people who live in Hawaii is 77 years.a random sample of 20 obituary notices gave a sample mean life span of x=71.4 years and a sample Standard deviation s=20.65 years.assuming that the population mean life span is less than 77 years? use a 5% level of significance.
a) what is a? state the null and alternate hypothesis.will you use a left- tailed, right- tailed, or two- tailed test?
b) identify the sampling distribution you will use.what is the value of the test statistic?
c) find or estimate the p- value.sketch the sampling distribution, show the area corresponding to the p- value.
d) conclude the test.state your conclusion in the context of the problem.
                  
                   

Explanation / Answer

Sola:

null hypothesis.

H0: mean=77

alternate hypothesis:

H1 mean<77

alpha=5%=0.05

its a left tail test

Solutionb:

given distribution is normal distribution.

SolutionC:

Here n=20

t=71.4-77/20.65/sqrt(20)

=-1.21

df=degrees of freedom=n-1=20-1=19

alpha=0.05

alpha/2=0.05/2=0.025

SolutionC:

The P-Value is .120559.

The result is not significant at p < .05.

Solutiond:

p>0.05

Fail to reject Null hypothesis

Accept null hypothesis.

Conclusion:

there is no sufficient statistical evidence at 5% level of significance to support the claim that

the population mean life span is less than 77 .

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