For each of the following, state (using symbols) the null and alternative hypotheses.
a. Is the mean IQ of a sample of 60 children significantly below the national average of 100?
b. Is the proportion of men in the class more than that expected by chance?
c. Does the mean speed of vehicles on the Thruway exceed 65?
d. Does the mean temperature level exceed 50 degrees?
e. Does the mean age of schoolchildren who have the measles differ from 11?
f. The persons in a weight loss diet group weigh themselves before beginning the diet. Five weeks later they each re-weigh and compute the difference: before – after. The group average difference is then computed. Is the diet successful in achieving weight loss?
a. For the IQ question, the null hypothesis (H0) would be that the mean IQ of the sample is not significantly below the national average of 100. The alternative hypothesis (Ha) would be that the mean IQ of the sample is significantly below the national average of 100. The symbols for these hypotheses would be:
H0: μ = 100
Ha: μ < 100
b. For the proportion of men question, the null hypothesis (H0) would be that the proportion of men in the class is equal to what would be expected by chance. The alternative hypothesis (Ha) would be that the proportion of men in the class is greater than what would be expected by chance. The symbols for these hypotheses would be:
H0: p = p0 (where p0 is the expected proportion by chance)
Ha: p > p0
c. For the mean speed of vehicles question, the null hypothesis (H0) would be that the mean speed of vehicles on the Thruway is not significantly greater than 65. The alternative hypothesis (Ha) would be that the mean speed of vehicles on the Thruway is significantly greater than 65. The symbols for these hypotheses would be:
H0: μ ≤ 65
Ha: μ > 65
d. For the mean temperature level question, the null hypothesis (H0) would be that the mean temperature level is not significantly greater than 50 degrees. The alternative hypothesis (Ha) would be that the mean temperature level is significantly greater than 50 degrees. The symbols for these hypotheses would be:
H0: μ ≤ 50
Ha: μ > 50
e. For the mean age of schoolchildren question, the null hypothesis (H0) would be that the mean age of schoolchildren with the measles is not significantly different from 11. The alternative hypothesis (Ha) would be that the mean age of schoolchildren with the measles is significantly different from 11. The symbols for these hypotheses would be:
H0: μ = 11
Ha: μ ≠ 11
f. For the weight loss diet question, the null hypothesis (H0) would be that the diet is not successful in achieving weight loss. The alternative hypothesis (Ha) would be that the diet is successful in achieving weight loss. The symbols for these hypotheses would be:
H0: μ = 0 (where μ is the population mean difference in weights)
Ha: μ < 0