Question

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

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

Step-by-step solution

Given Information

Given

the sample size $n=12$

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

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

Standard deviation of sample $\left(S\right)=\$0.18$

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

The mean of the population $\text{'}\mu \text{'}=\$1.00.$

Null hypothesis:-$H₀:\text{'}\mu \text{'}=\$1.00.$

Alternative hypothesis:$H₁:\text{'}\mu \text{'}\ne \$1.00.$

level of significance$\propto =0.01$

Explanation

The test statistic on calculation, we get

$t=-0.96$

$\left|t\right|=|-0.96|=0.96$

Degrees of freedom$\gamma =n-1=12-1=11$

$tₐ=2.718$

Calculated value $t=0.96$

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

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