Question

QUESTION 1 Let’s say that an investigator is interested in the effects of caring for a person with ALS (Lou Gehrig’s disease) on physical and mental health. In particular, the researcher wants to know whether ALS caregivers suffer from clinically elevated levels of depression. They administer the Beck Depression Inventory (BDI) to 20 ALS caregivers. Scores on the BDI range from zero to 40. Scores at or above 25 are considered to reflect clinically significant levels of depression. The mean depression score for the 20 caregivers in the sample is 28. The standard deviation for this sample is 3.0. Do these data support the hypothesis that the mean depression score for ALS caregivers is significantly higher than the cutoff score for depression of 25? This example is not a perfect example of a "true experiment," so the independent and dependent variable are not as clearly identifiable as some other examples. In this example, what is the dependent/outcome variable? Beck Depression Inventory scores How many ALS caregivers there are in the study Whether the caregivers are taking care of someone who has ALS vs. cancer The ALS caregivers vs. the national norms for adults

Answer 1

The decision rule is

Reject the null hypothesis

The conclusion is

There is sufficient evidence to conclude that the data support the hypothesis that the mean depression score for ALS caregivers is significantly higher than the cutoff score for depression of 25

dependent/outcome variable

Generally the dependent variable is Beck Depression Inventory (BDI) scores because the score are dependent on the ALS caregivers

Explanation:

From the question we are told that

The sample size is n = 20

The population mean is
`\mu  =  25`

The sample mean is
`\= x  = 28`

The standard deviation is
`s  =  3.0`

The null hypothesis is
`H_o  :  \mu  =  25`

The alternative hypothesis is
`H_a  :  \mu  >  25`

Generally the test statistics is mathematically represented as

`z = (\= x - \mu )/( (s)/(√(n) ) )`

=>
`z= ( 28 -25 )/( (3.0)/(√(20 ) ) )`

=>
`z=  4.47`

Generally the probability of z from the z- table is

`p-value  =  P(Z >  4.47) =  0.000`

From the values obtained we see that
`p-value  <  \alpha` hence

The decision rule is

Reject the null hypothesis

The conclusion is

There is sufficient evidence to conclude that the data support the hypothesis that the mean depression score for ALS caregivers is significantly higher than the cutoff score for depression of 25

Generally the dependent variable is Beck Depression Inventory (BDI) scores because the score are dependent on the ALS caregivers