Question

Show all five steps of the hypothesis test. You can either type them in here, or write them out on paper and send me a scan/picture of your work.The average movie ticket in 2010 cost $7.89. A random sample of 15 movie tickets from the suburbs of a large U.S. city indicated that the mean cost was $11.09 with a standard deviation of $4.86. At the 0.01 level of significance, can it be concluded that the mean in this area is higher than the national average?

Answer 1

Step 1

State the null and alternative hypothesis

`\begin{gathered} H_o=7.89 \\ H_a>7.89 \end{gathered}`

Step 2

State the p-value of the significance level.

`\begin{gathered} \alpha=0.01 \\ p=(\alpha)/(2)=(0.01)/(2)=0.005 \end{gathered}`

Step 3

Calculate the statistical test

The t-test formula is given as

`t=\text{ }\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}`

Where

`\begin{gathered} t=\frac{7.89-11.09}{\frac{4.86}{\sqrt[]{15}}} \\ t=(7.89-11.09)/(1.254846604) \\ t=(-3.2)/(1.254846604) \\ t=-2.550112492 \end{gathered}`

Step 4

Find the p-value from the t-test.

`\text{The p-value from the t-test is 0.01}209`

Step 5

Conclusion

The result is not significant at p<0.01. Therefore, the null hypothesis is rejected. It cannot be concluded that the mean in this area is higher than the national average because the p-value is greater than 0.01t