Question

The cost of a daily newspaper varies from city to city. However, the variation among prices remains steady with a population standard deviation of $0.20. 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 $0.93 with a standard deviation of $0.18. Do the data support the claim at the 1% level?

Answer 1

Yes, there is sufficient evidence to support the claim that the mean cost is $1.

Explanation:

Data Given:

The population standard deviation
`\sigma` = $0.2

The sample mean cost
`\bar {X}` = $0.93

The sample size n = 12

From above we can use the Z-test for testing the mean from the above given data.

To check whether the mean cost of newspaper is $1.00

`\mathbf{H_o}` :
`\mu` = $1

`\mathbf{H_1}` :
`\mu`
`\\eq` $1

The test statistics Z =
`\frac{\bar {X}- \mu}{(\sigma )/(√(n)) }`

Z =
`(0.93- 1)/((0.2)/(√(12)) )`

Z = -1.212

The P-value = 2P (Z< - 1.212)

= 2 × 0.1128

= 0.2256

Since the value of P is more than the significance level; do not reject the
`\mathbf{H_o}`

Conclusion: We therefore conclude that there is sufficient evidence to support the claim that the mean cost is $1.