A major television network is trying to determine whether to increase or decrease the number of news-based television shows. They conducted a national survey and found that their population watched 8 news shows each week. Now they need your help to determine if the mean number of news shows watched in your neighborhood is similar to the national mean.

What is your question?

Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√(n-1)

If only one SD is provided, you can use just that to determine SEdiff.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to your Z score to compare it to your level of significance.

To determine if the mean number of news shows watched in your neighborhood is similar to the national mean, you can conduct a hypothesis test. Here's how you can do it:

1. Formulate your hypotheses:
- Null Hypothesis (H0): The mean number of news shows watched in your neighborhood is similar to the national mean.
- Alternative Hypothesis (Ha): The mean number of news shows watched in your neighborhood is different from the national mean.

2. Collect data:
- Survey a random sample of residents in your neighborhood and ask them how many news shows they watch each week.
- Make sure your sample size is large enough to meet the normality assumption, aiming for a sample size of at least 30.

3. Calculate the sample mean:
- Find the average (mean) number of news shows watched among your sample.

4. Determine the significance level (alpha):
- Choose a significance level for your hypothesis test, typically 0.05 (5%).

5. Compute the test statistic:
- Use either a Z-test or t-test, depending on whether you know the standard deviation of the population or not.
- If you know the population standard deviation, use the Z-test. If not, use the t-test and estimate the standard deviation from your sample.

6. Find the critical value:
- Look up the critical value associated with your chosen significance level and degrees of freedom (n-1) in the appropriate statistical table.
- This critical value will help you determine whether to reject or fail to reject the null hypothesis.

7. Conduct the hypothesis test:
- Compare your test statistic with the critical value.
- If the test statistic falls within the range of the critical values, fail to reject the null hypothesis. This suggests that the mean number of news shows watched in your neighborhood is similar to the national mean.
- If the test statistic falls outside the range of the critical values, reject the null hypothesis. This suggests that the mean number of news shows watched in your neighborhood is different from the national mean.

8. Interpret the results:
- Based on your analysis, make a conclusion about whether the mean number of news shows watched in your neighborhood is similar to the national mean or not.

Remember, hypothesis testing is a statistical procedure that helps you make an inference about a population based on a sample. The key is to collect reliable data and apply the appropriate statistical test to evaluate your hypothesis.