Consider the following: 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.
• Before moving to the next step, determine if you think your neighborhood will watch fewer news shows, more news shows, about the same number of news shows or a different number of news shows (either more or less). You may base your answer on your opinion.
• Find a deck of cards and remove the kings. Ask a friend or family member to draw 3 cards. Ace represents 1, Jack represents 11, and Queen represents 12. If you cannot locate a deck of cards, find a pair of dice, and roll them 3 times. If you do not have cards or dice, ask 3 friends to each choose a number between 1 and 12. In any of these cases, you will have 3 numbers. Write them down.
• Determine the mean for your 3 numbers. They represent your neighborhood's news-viewing habits. The mean is the number of news programs viewed in your neighborhood each week. Keep in mind that you would typically have a much larger sample size than 3. With these thoughts in mind: Post by Day 4 the mean for your 3 numbers. Then respond briefly to each of the following questions about your findings:
• How did you think that your sample would compare to the national mean? This is your hypothesis. State either the alternate or null hypothesis and identify which one you are stating.
• Based on your hypothesis, would you use a one-tailed or two-tailed test? Explain why.
• Remember that your sample was very small at 3. With a sample of 3, your degrees of freedom would be 2. Imagine you could have sampled many more people in your neighborhood. Post the number of people you would really want to sample if you could. Consider this your ideal N.
• Imagine that you had your ideal N. Your alpha level was .05. Choose a one or two-tailed test as appropriate, and look up the critical value of t. State the value in your post.
• What would you conclude if your obtained t was larger than your critical t value, and what you conclude if your obtained t was smaller than your critical value? The 3 cards drawn were 3, 7, and 1 (An ace).