According to a Louis Harris poll, 63% of men drivers always use seat belts. A recent sample of 900 men drivers showed that 60% of them always use seat belts. Test at the 1% significance level if the proportion of men drivers who always use seat belts is less than .63
To test whether the proportion of men drivers who always use seat belts is less than 0.63, we can perform a hypothesis test using the sample data.
Here are the steps to conduct the hypothesis test:
1. State the null hypothesis (H0): The proportion of men drivers who always use seat belts is equal to or greater than 0.63.
2. State the alternative hypothesis (Ha): The proportion of men drivers who always use seat belts is less than 0.63.
3. Select the significance level (α) for the test. In this case, the significance level is given as 1%, which means α = 0.01.
4. Collect the data. From the problem statement, we are given a recent sample of 900 men drivers, and 60% of them always use seat belts.
5. Calculate the test statistic. The test statistic for this hypothesis test is the z-score. The formula for the z-score is z = (p̂ - p0) / √[(p0 * (1 - p0)) / n], where p̂ is the sample proportion, p0 is the hypothesized proportion under the null hypothesis, and n is the sample size. In this case, p̂ = 0.60, p0 = 0.63, and n = 900.
z = (0.60 - 0.63) / √[(0.63 * (1 - 0.63)) / 900]
Calculate the result to find the value of the test statistic.
6. Determine the critical value. The critical value is the value that separates the rejection region from the non-rejection region. Since the alternative hypothesis is that the proportion is less than 0.63, we will use a one-tailed test. Lookup the critical value corresponding to a significance level of 0.01 (α = 0.01) in the standard normal distribution table.
7. Compare the test statistic and the critical value. If the test statistic is less than the critical value, we reject the null hypothesis. If the test statistic is greater than or equal to the critical value, we fail to reject the null hypothesis.
8. Make a conclusion. Based on the result, we either reject the null hypothesis or fail to reject it. In this case, if the test statistic is less than the critical value, we can conclude that there is evidence to support the claim that the proportion of men drivers who always use seat belts is less than 0.63.
Note: To find the critical value, you will need to use a standard normal distribution table or a statistical software.