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

Answer:

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

Step-by-step 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

$\mathbf{H_1}$ : $\mu$  $\neq$ $1

The test statistics Z = $\frac{\bar {X}- \mu}{\frac{\sigma }{\sqrt{n}} }$

Z = $\frac{0.93- 1}{\frac{0.2}{\sqrt{12}} }$

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.