Question 1
Hypothesis testing has been in existence for more than a century. Recently, statisticians have attacked its usage terming the concept as useless. One such criticism is that, hypothesis testing has no interesting applications.
However, there is a very close relationship between hypothesis testing and confidence intervals. For instance, during the construction of a 95% confidence interval, the values within the interval are considered to be plausible values for the parameter that is being estimated. Nonetheless, the values found outside the interval are rejected because they are considered to be relatively implausible. If the values of the parameters specified by the null hypothesis is found within the 95% interval, the null hypothesis, therefore, cannot be overruled at 5% interval level. However, if the values itemized by the null hypothesis is not within the interval, then the hypothesis can be rejected at 5% interval level. Therefore, the idea of not teaching hypothesis testing has no merit.
Question 2.
a). Find the probability that heights of the males is less than 66 inches
Given that, Z = (x – μ)/σ
Z (66) = (66-69.2)/2.9 = -1.1
P(x < 66) = P (z < -1.1) = normal cdf (-100,-1.1) = 0.1357
= 13.57%
b). Find the probability that his height is between 66 and 72 inches
Given that, Z = (x – μ)/σ
Z (72) = (72-69.2)/2.9 = 0.97
P (66< x <72) = P (-0.97< z <-1.1) = normal cdf (-0.97, -1.1) = 0.0303
= 3.03%
c). Find the probability that his height is more than 72 inches.
P(x > 72) = P (z > 0.97) = normal cdf (0.97, 100) = 0.8340 = 83.4%
