1. identify the independent and dependent variables 2. give the null and alterna

ID: 3231211 • Letter: 1

Question

1. identify the independent and dependent variables

2. give the null and alternative hypothesis

3. determine the critical value (use alpha = .05)

4. calculate the F statistic and all the required intermediate steps

A student interested in alternative sleep aids has heard that valerian root, melatonin and 5-htp have very few side effects and may be able to help with her recent insomnia. She decides to run a little experiment with her sorority sisters to determine which of the three makes people fall asleep the fastest. The following data is the amount of time, in minutes, between consumption and sleep for each of the three natural sleep aids.

Valerian Root

Melatonin

5- HTP

Valerian Root

Melatonin

5- HTP

Explanation / Answer

1. identify the independent and dependent variables

Answer: The dependent variable for this research study is given as amount of time in minutes, between consumption and sleep and independent variable is given as the type of sleep aids.

2. give the null and alternative hypothesis

Answer: The null and alternative hypothesis for this study is given as below:

Null hypothesis: H0: There is no any significant difference in the average amount of time between consumption and sleep for the three natural sleep aids.

Alternative hypothesis: Ha: There is a significant difference in the average amount of time between consumption and sleep for the three natural sleep aids.

In symbolic form, it is given as below:

H0: µ1 = µ2 = µ3 versus Ha: µ1 µ2 µ3 or Ha: µ1 = µ2 µ3 or Ha: µ1 µ2 = µ3

3. determine the critical value (use alpha = .05)

Answer:

For finding critical value, we have to find degrees of freedom for F value.

Number of factors = 3

So, upper or between groups degrees of freedom = 3 – 1 = 2

Total number of observations = n = 30

Total degrees of freedom = n – 1 = 30 – 1 = 29

Within groups degrees of freedom = total degrees of freedom – between degrees of freedom = 29 – 2 = 27

Level of significance = alpha = 0.05

So, we have to find F critical value with df1 = 2, df2 = 27 and = 0.05

So, by using F-table,

Critical value = F = 3.354131

4. calculate the F statistic and all the required intermediate steps

Answer:

Here, we have to find F test statistic value. The table for required values and ANOVA table is given as below:

Groups

Count

Sum

Average

Variance

Valerian Root

303

30.3

7.788889

Melatonin

341

34.1

7.655556

5- HTP

294

29.4

6.488889

ANOVA

Source of Variation

P-value

F crit

Between Groups

124.4667

62.23333

8.512158

0.00136

3.354131

Within Groups

197.4

7.311111

Total

321.8667

F = 62.23333/7.311111 = 8.512158

F statistic = 8.512158

Here, we get p-value = 0.00136 < Alpha value = 0.05.

So we reject the null hypothesis that there is no any significant difference in the average amount of time between consumption and sleep for the three natural sleep aids.

We conclude that there is sufficient evidence that there is a significant difference in the average amount of time between consumption and sleep for the three natural sleep aids.