Deck 6: Introduction to Hypothesis Testing: Inferences About a Single Mean

Question 1

Using this random sample of data, test the following hypothesis at the .05 level of significance using SPSS. Interpret the output including identifying the specific statistical procedure that has been used and reporting the extent to which the test is statistically significant. Include appropriate evidence (e.g., values from the output).

DATA
21.00
16.00
12.00
8.00
9.00
4.00
7.00
2.00
9.00
11.00
15.00
10.00
7.00
14.00
10.00
17.00
8.00
3.00
2.00
6.00

$\begin{array}{l}H_{0}: \mu=10 \\H_{1}: \mu \neq 10\end{array}$

Answer 1

A one-sample t test was conducted. The results are not statistically significant, t = -.390, df =19, p = .701.

$\begin{array}{c}\text { One-Sample Statistics }\\\begin{array}{|l|r|r|r|r|}\hline & {N} & {\text { Mean }} & \text { Std. Deviation } & \text { Std. Error Mean } \\\hline \times & 20 & 9.5500 & 5.15522 & 1.15274 \\\hline\end{array}\end{array}$

Question 2

Using this random sample of data, test the following hypothesis at the .05 level of significance using SPSS. Interpret the output including identifying the specific statistical procedure that has been used and reporting the extent to which the test is statistically significant. Include appropriate evidence (e.g., values from the output).

DATA
45.00
50.00
62.00
55.00
36.00
22.00
51.00
38.00
47.00
40.00
58.00
59.00
52.00
68.00
65.00
45.00
30.00
35.00
47.00
54.00

$\begin{array}{l}H_{0}: \mu=50 \\H_{1}: \mu \neq 50\end{array}$

Answer 2

A one-sample t test was conducted. The results are not statistically significant, t = -.767, df =19, p = .453.

$\begin{array}{c}\text { One-Sample Statistics }\\\begin{array}{|l|r|c|r|r|}\hline & {\mathrm{N}} & \text { Mean } & \text { Std. Deviation } & \text { Std. Error Mean } \\\hline \times & 20 & 47.9500 & 11.95815 & 2.67392 \\\hline\end{array}\end{array}$

Question 3

When testing the hypothesis presented below, at a .05 level of significance with the t test, where is the rejection region?

$\begin{array}{l}H_{0}: \mu=100 \\H_{1}: \mu>100\end{array}$

A) The upper tail
B) The lower tail
C) Both the upper and tails
D) Cannot be determined

Answer 3

The upper tail

Question 4

When testing the hypothesis presented below, at a .05 level of significance with the t test, where is the rejection region?

$\begin{array}{l}H_{0}: \mu=100 \\H_{1}: \mu \neq 100\end{array}$

A) The upper tail
B) The lower tail
C) Both the upper and tails
D) Cannot be determined

Question 5

Which of the following conditions must be met with the one sample t test?

A) Expected frequencies greater than 5
B) Interval or ratio dependent variable
C) Independent variable with two categories
D) Sample size greater than 30

Question 6

The assumption of independence for the one sample t test calls for having which of the following?

A) Equal sample sizes
B) Random assignment
C) Random selection of the sample from the population
D) Sample size greater than 30

Question 7

A researcher conducts a one sample t test with a sample of 26 individuals. What are the degrees of freedom for this study?

A) 24
B) 25
C) 26
D) Cannot be determined