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Chapter 9: Q.76 (page 543)

The cost of a daily newspaper varies from city to city. However, the variation among prices remains steady with a

standard deviation of 20¢. A study was done to test the claim that the mean cost of a daily newspaper is $1.00. Twelve costs

yield a mean cost of 95¢ with a standard deviation of 18¢. Do the data support the claim at the 1% level?

Short Answer

Expert verified

The data support the claim that the mean cost of a daily news paper is $1.00

Step by step solution

01

Given Information

Given

the sample size n=12

Twelve costs yield a mean cost of $0.95with a standard deviation of $0.18

mean of the samplelocalid="1650204298826" (x⁻)=$0.95

Standard deviation of sample (S)=$0.18

Given claim that the mean cost of a daily newspaper is $1.00.

The mean of the population 'μ'=$1.00.

Null hypothesis:-H₀:'μ'=$1.00.

Alternative hypothesis:H₁:'μ'≠$1.00.

level of significance∝=0.01

02

Explanation

The test statistic on calculation, we get

t=-0.96

|t|=|-0.96|=0.96

Degrees of freedomγ=n-1=12-1=11

tₐ=2.718

Calculated value t=0.96

Tabulated value t=0.01level for 11°for two tailed test = 2.718

since calculated' t' value is less than tabulated value 't'.

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