Chapter 11, Problem 1CQQ

Exercises 1-5 refer to the sample data in the following table, which summarizes the last digits of the heights (cm) of300 randomly selected subjects (from Data Set 1 “Body Data” in Appendix B). Assume that we want to use a 0.05 significance level to test the claim that the data are from a population having the properly that the last digits are all equally likely.

1. What are the null and alternative hypotheses corresponding to the stated claim?

To determine

To identify: The null and alternate hypotheses.

Answer to Problem 1CQQ

The null Hypothesis, $\underset{\_}{H_0:p_0=p_1=p_2=p_3=p_4=p_5=p_6=p_7=p_8=p_9=\frac{1}{10}}$

The alternative hypothesis, $H_1$ is at least one of the proportions is not equal to the given claim.

Explanation of Solution

Given info:

The dataset shows the heights in cm of 300 randomly chosen subjects. Assume to test the claim that thedata is taken from a population having the last digits which are equally likely to occur at 5% level of significance.

Justification:

Since, there are digits from 0 to 9, there are 10 digits. The claim is to test whether the last digit are equally likely to occur. Each of the digits has equal chance to occur as last digit. Thus, the probability for each digit to occur as last digit has equal probability which is $\frac{1}{10}$.

Hence, the null hypothesis is,

$\underset{\_}{H_0:p_0=p_1=p_2=p_3=p_4=p_5=p_6=p_7=p_8=p_9=\frac{1}{10}}$

If the claim is false, then at least one of the digits is different from the given probability of occurrence $\frac{1}{10}$. Hence, the alternative hypothesis is,

$H_1:$ At least one of the proportions is not equal to the given claim.