Chapter 10 Hypothesis Tests Regarding a Parameter

Question 1

Notation for the Probability of Making a Type I Error

Answer 1

α = p(Type I error) = p(rejecting Ho when Ho is true)

Question 2

Notation for the Probability of Making a Type II Error

Answer 2

β = p(Type II error) = p(not rejecting Ho when H1 is true)

Question 3

Level of Significance

Answer 3

The probability of making a Type I error. Denoted by α.

Question 4

What determines a researcher’s choice of the level of significance?

Answer 4

The choice of the level of significance depends on the consequences of making a Type I error. If the consequences are severe, the level of significance should be small (say, α=0.01). However, if the consequences are not severe, a higher level of significance can be chosen (say, α=0.05 or α=0.10).

Question 5

What is the relation between a Type I error and a Type II error?

Answer 5

As the probability of a Type I error increases, the probability of a Type II error decreases (inverse).

Question 6

We never reject the null hypothesis. Why?

Answer 6

Without having access to the entire population, we do not know the exact value of the parameter stated in the null hypothesis.

Question 7

P-value

Answer 7

The probability of observing a sample statistic as extreme as or more extreme than one observed under the assumption that the statement in the null hypothesis is true.

Question 8

Hypothesis Testing Using the P-Value Approach

Answer 8

If the probability of getting a sample statistic as extreme as or more extreme than the one obtained is small under the assumption that the statement in the null hypothesis is true, reject the null hypothesis.

Question 9

Method for Testing Hypotheses Regarding a Population Proportion p

Answer 9

1. Determine null and alternative hypotheses
2. Select a level of significance
3. Compute the test statistic and P-value
4. Decision about the null hypothesis (If the P-value is less than alpha, reject the null hypothesis)

Question 10

Three Conditions That Must Be Met Before Hypothesis Testing Can Proceed

Answer 10

1. Sample is obtained from a simple random sampling
2. np sub-zero(1 - p sub-zero) is greater than or equal to 10
3. Sample values are independent: n less than or equal to 0.05N

Question 11

Method for Testing Hypotheses Regarding a Population Proportion p Using TI-84 Calculator

Answer 11

STAT > TESTS > 5: 1-propZTest
Enter the values for p sub-zero, x, and n
Select the appropriate alternative hypothesis
Highlight Calculate: press ENTER

Question 12

Testing a Hypothesis Using a Confidence Interval

Answer 12

STAT > TESTS > A: 1-propZInt
Enter values of x an n
Enter the confidence level following C-Level:
Highlight Calculate: press ENTER

Question 13

p-naught

Answer 13

The symbol p-naught represents the population proportion according to the null hypothesis. If the null hypothesis is​ true, then p-naught = p.