Question

The website Data USA stated that in 2016, adults older than 18 in the US population reported an average of 14.5 on the Beck Depression Inventory (BDI); the standard deviation was unknown. The state of Texas wants to determine if the mean number of symptoms on the BDI endorsed by 36 randomly selected residents (M = 17.0; SD = 2.5) is significantly higher than the population mean. The alpha level for the study was set to α=.05 for the criteria.

a. State the hypotheses of the study.

b. Find the critical t value for this study

c. Compute the one sample t test

d. Compute the Cohen's d for the data

e. State the results in APA format (numbers and words) and don’t forget to include all parts in the sentence and the direction of the results.

Answer 1

(a)

H0: Null Hypothesis: 14.5 ( the mean number of symptoms on the BDI endorsed by 36 randomly selected residents (M = 17.0; SD = 2.5) is not significantly higher than the population mean )

HA: Alternative Hypothesis: 14.5 ( the mean number of symptoms on the BDI endorsed by 36 randomly selected residents (M = 17.0; SD = 2.5) is significantly higher than the population mean ) (Claim)

(b)

= 17.0

s = 2.5

n = 36

= 0.05

df = 36 - 1 = 35

From Table, critical value of t = 1.69

(c)

Test Statisticis given by:

(d)

Cohen's d is given by:

(e)

The Research Question taken up for study was: Is the mean number of symptoms on the BDI endorsed by the State of Texas is significantly higher than the population mean.?. For answering this question, 1 Sample t test was conducted. First data on number of symptoms on the BDI endorsed by 36 randomly selected residents was collected and its statistics were computed: M = 17.0; SD = 2.5. Test Statstic was got as t = 6.00, which is greater than critical value of t = 1.69. The difference issignificant. Reject null hy[pothesis. We conclude that the data support the claim that the mean number of symptoms on the BDI endorsed by 36 randomly selected residents (M = 17.0; SD = 2.5) is significantly higher than the population mean.