Chapter 11 Introduction To Hypothesis Testing

Question 1

Hypothesis testing

Answer 1

Determining whether there is enough statistical evidence to conclude a hypothesis about a parameter is supported by the data

Tests two hypotheses:
Null hypothesis H0: default “conclusion”
Alternative or research hypothesis H1: thing you’re trying to determine if there is evidence to support

If sufficient evidence to support H1: reject the null hypothesis in factor of the alternative

If lack sufficient evidence: not rejecting the null hypothesis

Question 2

Type I error

Answer 2

Rejecting a true null hypothesis

Probability denoted by alpha

Alpha is inverse of beta (1-beta = alpha)

Probability of type I error: significance level

Question 3

Type II error

Answer 3

Not rejecting a false null hypothesis

Probability denoted by beta

Inverse of alpha (1-alpha = beta)

Question 4

Null hypothesis form

Answer 4

Always states that the parameter equals the value specified in the alternative hypothesis

So always H0=

Question 5

Test statistic

Answer 5

Statistic calculated from a random sample of the population on which to test a hypotheses

Statistic should be best for estimate of the parameter

If test statistic’s value is inconsistent with the null hypothesis we reject the null hypothesis and infer that the alternative hypothesis is true

Question 6

Rejection region

Answer 6

A range of values such that if the test statistic falls into that range we decide to reject the null hypothesis in favor of the alternative hypothesis

For standardized test statistic the rejection region is all values of z greater than za, where a is the significance level (probability estimation method will be wrong)

Direction of inequality in the rejection region (z< or > za) matches the direction of the inequality in the alternative hypothesis

If positive za rejection region is in the right tail, negative za rejection region in the left tail

Question 7

Significance level

Answer 7

How frequently the estimating procedure will produce an answer that will be wrong

For determining the rejection region for hypothesis testing the significance level is the a in Z>Za

Question 8

Standardized test statistic

Answer 8

Z= (mean of x minus population mean)/ (standard deviation / sqroot of n)

Question 9

Statistically significant

Answer 9

When a null hypothesis is rejected the test is said to be statistically significant at the significance level at which the test was conducted

Question 10

P- value

Answer 10

The p-value of a test is the probability of observing a test statistic at least as extreme as the one computed given that the null hypothesis is true

Calculate p(xbar > specific value of xbar)

• convert xbar and value to z format to get p(z>result)
• Use table to find probability z < result and subtract to get complement

Question 11

Interpreting the p value

Answer 11

Says that the probability of observing a statistic of x from a population whose parameter is the null hypothesis value is the p value

NOT the probability the null hypothesis is true. (Cannot make a probability statement about a parameter)

Smaller p value = more support for alternative hypothesis

Question 12

Describing the p value

Answer 12

P-value < 0.01 = test is highly significant (overwhelming evidence the alternative hypothesis is true)

0. 01 < P-value < 0.05 = test is significant (there is strong evidence the alternative hypothesis is true)
1. 05 < P-value < 0.1 = test is not statistically significant (there is weak evidence that the alternative hypothesis is true)

P-value > 0.1 = little to no evidence to infer alternative hypothesis is true

Question 13

Conclusions of a test of hypothesis

Answer 13

If we reject the null hypothesis, we conclude that there is enough statistical evidence to infer that the alternative hypothesis is true.

If we do not reject the null hypothesis, we conclude that there is not enough statistical evidence to infer that the alternative hypothesis is true. (If the value of the test statistic does not fall into the rejection region)

Never actually proving alternative hypothesis is true via statistical inference

Question 14

One-tail tests

Answer 14

When the rejection region is located in only one tail of the sampling distribution

P value computed by finding the area in one tail of the distribution

Alternative hypothesis specifies greater than : right tail

Alternative hypothesis specifies less than : left tail

Question 15

Two-tail tests

Answer 15

Conducted when the alternative hypothesis specifies the mean is not equal to the value stated in the null hypothesis

Requires looking at both the left and right tails of the sampling distribution

This two-tail rejection region requires that a be divided by two (because total area in rejection region must = a)
Because z< -za or z> za