2. A TV pollster believed that 70% of all TV households would be tuned in to Game 6 of the 1997 NBA Championship series between the Chicago Bulls and the Utah Jazz. A random sample of 500 TV households is selected.
TV households is selected.
To analyze the data and determine whether the TV pollster's belief is accurate, we need to perform a hypothesis test.
Here are the steps to carry out the hypothesis test:
1. Define the null hypothesis (H0) and alternative hypothesis (Ha):
- Null Hypothesis (H0): The proportion of TV households tuned in to Game 6 is equal to 70% (p = 0.70).
- Alternative Hypothesis (Ha): The proportion of TV households tuned in to Game 6 is not equal to 70% (p ≠ 0.70).
2. Calculate the sample proportion (p̂):
- The sample proportion represents the proportion of the 500 TV households sampled that were tuned in to Game 6.
3. Calculate the test statistic z:
- The test statistic z is calculated using the formula: z = (p̂ - p) / √(p * (1-p) / n)
- p̂ is the sample proportion.
- p is the hypothesized proportion.
- n is the sample size.
4. Define the significance level (α):
- The significance level determines the threshold for accepting or rejecting the null hypothesis.
- In this case, let's assume a significance level of 0.05 (or 5%).
5. Determine the critical values or p-value:
- Critical values are obtained from the standard normal distribution table based on the significance level and the test being two-tailed.
- The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true.
6. Compare the test statistic with the critical values or p-value:
- If the test statistic falls within the critical values or the p-value is less than the significance level, we reject the null hypothesis.
- If the test statistic falls outside the critical values or the p-value is greater than the significance level, we fail to reject the null hypothesis.
Using these steps, we can analyze the data and draw a conclusion regarding the TV pollster's belief about the proportion of TV households tuned in to Game 6 of the 1997 NBA Championship series.