Question

question 18
1 pts
ch 21* a study of the effect of exposure to color (red or blue) on the ability to solve puzzles used 42 subjects. half the subjects (21) were asked to solve a series of puzzles while in a red - colored environment. the other half were asked to solve the same series of puzzles while in a blue - colored environment. the time taken to solve the puzzles was recorded for each subject. to compare the mean times for the two groups of subjects using the two - sample t procedures, the correct degrees of freedom is
41
20
40
question 19
1 pts
ch 21* the two - sample t statistic for the social media use study (\under 40\ mean minus \40 and over\ mean) is t = 3.18 with df = 420. the p - value for testing the hypotheses that younger adults use social media more than adults aged 40 or over. satisfies
0.0005 < p < 0.001.
0.001 < p < 0.005.
0.001 < p < 0.002.

Explanation:

Question 18

Step1: Degrees of freedom formula for two - sample t - test

For a two - sample \(t\) - test with sample sizes \(n_1\) and \(n_2\), the degrees of freedom using the conservative (smaller) estimate (when variances are unknown and assumed unequal) is \(df=\min(n_1 - 1,n_2 - 1)\). Here \(n_1=n_2 = 21\).

$$n_1-1=21 - 1=20$$

$$n_2-1=21 - 1=20$$

Question 19

Step1: Locate the \(t\) - value in the \(t\) - distribution table

We have a one - sided (right - tailed, since we are testing if younger adults use social media more, i.e., \(\mu_{under40}-\mu_{40 +}>0\)) \(t\) - test with \(t = 3.18\) and \(df = 420\).
For large degrees of freedom (\(df\geq100\)), the \(t\) - distribution is very close to the standard normal distribution.
Looking at the standard normal table (or using a calculator with \(t\) - distribution functions), for a one - tailed test:
If \(t = 3.18\), and using the fact that for \(z\) (approximate \(t\) for large \(df\)):
\(P(Z>3)=0.0013\) and \(P(Z > 3.29)=0.0005\)

Answer:

Question 18: 20
Question 19: \(0.0005