Deck 8: From Estimation to Statistical Tests: Hypothesis Testing for One Population Mean and Proportion

Question 1

Why is probability theory needed rather than assuming that a finding is different from that of the population?

A) Due to sampling variation a sample will always be at least slightly different from the population
B) To be 100% sure that our findings are correct
C) To say that our independent variable unquestionably causes the dependent variable
D) Confidence intervals are not enough to be certain of our findings

Answer 1

A

Question 2

The null hypothesis always ______.

A) assumes there is a relationship between the independent and dependent variables
B) assumes there is no relationship between the independent and dependent variables
C) helps us be 100% certain our findings are real
D) can be proven wrong

Answer 2

B

Question 3

What type of hypothesis is a researcher stating when they say "I hypothesize that the independent variable influences the dependent variable"?

A) directional alternative hypothesis test (one-tailed)
B) negative directional alternative hypothesis test
C) positive directional alternative hypothesis test
D) nondirectional alternative hypothesis test (two-tailed)

Answer 3

D

Question 4

Which of the following is a correctly stated null hypothesis?

A) H₀: $\mu$ $\neq$ 10
B) H₀: $\mu$ = 10
C) H₀ $\bar{X}$ > 10
D) H₀: $\bar{X}$ < 10

Question 5

The statement ______ is an example of a ______.

A) $\mu$ ? 5; null hypothesis
B) $\mu$ > 5; null hypothesis
C) $\mu$ < 5; null hypothesis
D) $\mu$ = 5; null hypothesis

Question 6

What type of hypothesis is a researcher stating when they say "I hypothesize that the independent variable positively influences the dependent variable"?

A) directional alternative hypothesis test (one-tailed)
B) nondirectional alternative hypothesis test
C) negative directional alternative hypothesis test
D) nondirectional alternative hypothesis test (two-tailed)

Question 7

Using the first step in hypothesis testing, how would one represent the following statement from a researcher, "I hypothesize that my sample mean is different from the population mean"?

A) $H_{o}: \bar{X}=\mu$
$H_{1}: \bar{X} \neq \mu$
B) $H_{o}: \bar{X}=\mu$
$H_{1}: \bar{X}>\mu$
C) $H_{o}: \bar{X}=\mu$
$H_{1}: \bar{X}<\mu$
D) $H_{o}: \bar{X}=\mu$
$H_{1}: \bar{X} \geq \mu$

Question 8

For a two-tailed hypothesis test with a significance alpha level of .05, what is the critical z-value?

A) $\pm$ 3.08
B) $\pm$ 1.96
C) +1.95
D) -1.96

Question 9

6. In the figure below, one would reject the null hypothesis if ______.

A) the z/t-value fell into the unshaded region
B) the z/t-value fell into the shaded region
C) the z/t-value fell directly on the middle of the distribution
D) the z/t-value fell right before entering the shaded region

Question 10

The distribution below illustrates which of the following?

A) one-tailed null hypothesis
B) nondirectional null hypothesis
C) directional alternative hypothesis
D) two-tailed alternative hypothesis

Question 11

In the distribution below, for a one-tailed alternative hypothesis test at an alpha level of 0.05, which z critical value would allow us to reject the null hypothesis?

A) $z=-1.65$
B) $z=1.65$
C) $z=\pm 1.65$
D) Unidentifiable

Question 12

Deciding to use a directional versus nondirectional alternative hypothesis most directly affects ______.

A) the standard deviation
B) the sample size
C) the critical value(s)
D) the degrees of freedom

Question 13

For a sample size of 29, we would rely on the ______.

A) z-distribution
B) t-distribution
C) either z- or t-distribution
D) neither z- or t-distribution

Question 14

For a sample size of 30, we would rely on the ______.

A) z-distribution
B) t-distribution
C) either z- or t-distribution
D) neither z- or t-distribution

Question 15

A researcher calculates a mean from a sample of 37 people. The following hypotheses are stated: H₀: $\mu$ = 40 and H₁: $\mu$ $\neq$ 40. For $\alpha$ = .05, what is an appropriate critical value for his statistic?

A) $\pm$ 2.00
B) $\pm$ 1.96
C) -1.65
D) -1.6

Question 16

When a researcher selects a particular alpha level, they are selecting the risk they are willing to take of making a Type II error.

Question 17

The z- and t-distributions have nearly identical critical values when the sample size is over 120.

Question 18

Because proportions are not whole numbers, the critical values for proportions are different than whole numbers.

Question 19

Because the t- and z-distributions use different distributions, there respective equations for testing hypotheses are different.

Question 20

The critical value of t at a given alpha level will be smaller than the comparable critical value of z and is much smaller when n is very small.

Question 21

The following equation, $\frac{p-p}{\sqrt{\frac{P(1-P)}{n}}}$ , is used for obtaining the critical value for proportions.

Question 22

We hypothesized that our sample mean of 58.5 is larger than the population mean of 52.5. This is can be graphed in the following manner.

Question 23

Discuss the five steps in hypothesis testing.

Question 24

Using distributions for visual depiction, draw out a two-tailed hypothesis test that your sample mean is different from that of the population. Draw out a one-tailed hypothesis test that your sample mean is smaller than that of the population. Draw out a one-tailed hypothesis test that your sample mean is larger than that of the population.