Question

In a measure of well-being, the state in which I live had a mean well-being score of 65.5 with a standard deviation of 1.6. I wonder if the people within my neighborhood would be significantly different from the state statistics. So I calculate the well-being scores for 16 within my neighborhood to run a statistical comparison. The data are presented below. What is the dependent variable and independent variable in this statistical test?

Subject	Well-being Score
1	68
2	78
3	64
4	71
5	67
6	66
7	68
8	57
9	65
10	49
11	68
12	71
13	69
14	64
15	68
16	66

Group of answer choices

DV-My neighborhood; IV-Level of well-being

DV-Well-being; IV-state

DV-Location (state or my neighborhood); IV-Level of well-being

DV-Level of well-being; IV-Location (state or my neighborhood)

Question 2 1 pts

What would be the null hypothesis for my statistical test? Note that I am interested in examining any difference between my sample and the population statistics and I am not predicting or hypothesizing any particular direction of the difference.

Group of answer choices

Level of well-being in my neighborhood is not significantly different from the general level of well-being in my state.

Level of well-being in my neighborhood is significantly different from the general level of well-being in my state.

Level of well-being in my neighborhood is significantly higher from the general level of well-being in my state.

Level of well-being in my neighborhood is not significantly higher from the general level of well-being in my state.

Question 3 1 pts

In order to compare the sample I collected (the well-being scores from my neighborhood) to the state statistics, calculate the mean of the sample. (Round it to 1 decimal place.)

Question 4 1 pts

Because a sample should be compared to a population of samples, we need to turn the original well-being scores from the state into a sampling distribution, which is composed of all the possible samples drawn from the whole state population of well-being scores. In order to position my sample on that sampling distribution, we need to know the standard deviation of the sampling distribution, which is also commonly called standard error (SE). Calculate SE from the state well-being statistics provided in the research scenario: mean (μ) = 65.5, SD (σ) = 1.6, along with the sample size N = 16. (Round it to 1 decimal place)

Question 5 1 pts

Now we need to locate our sample mean on the sampling distribution and see if it falls into an extreme (significance) area. If so, we would be able to reject the null hypothesis and say that the well-being scores in my neighborhood are indeed significantly different from the state well-being scores. To figure out the position of our sample mean on the sampling distribution, calculate the Z statistic for our sample. (Report to two decimal places.)

Question 6 1 pts

In the previous question, we calculated the Z statistic, which indicates where our sample mean is located in the sampling distribution. Now we need to find the critical Z value from the Z table so that we can see if the Z statistic (calculated from the sample mean) is more extreme than the critical Z value (the cut-off point) for the significance area. But before identifying the critical Z value, we need to first determine whether we will have the significance area in one tail or two tails, based on the hypotheses?  In other words, is the hypothesis test two-tailed or one-tailed?

Group of answer choices

Two-tailed

One-tailed

Either one-tailed or two-failed would work

We don't have sufficient information to make the decision.

Question 7 1 pts

Use the Z table to identify the critical Z value(s) for the type of hypothesis test selected, based on α = .05.

Group of answer choices

+1.96 and -1.96

+1.645 and -1.645

+1.96

+1.645

Question 8 1 pts

Now we determine whether our Z statistic (calculated from the sample mean) would fall into the significance area of the comparison sampling distribution, by comparing the Z statistic to the critical Z value (cut-off). Based on the Z statistic and critical Z value obtained in previous questions, what is the result of the hypothesis test?

Group of answer choices

We fail to reject the null hypothesis because the calculated Z is less extreme than the critical Z value.

We fail to reject the null hypothesis because the calculated Z is more extreme than the critical Z value.

We reject the null hypothesis because the calculated Z is less extreme than the critical Z value.

We reject the null hypothesis because the calculated Z is more extreme than the critical Z value.

Question 9 1 pts

The decision of rejecting the null hypothesis or failing to reject the null hypothesis does not directly answer the research question so it is always necessary to reiterate the analysis result by directly answering the research question. Which of the following answers is consistent with the hypothesis test result?

Group of answer choices

The well-being scores in my neighborhood are not significantly different from the well-being scores in the state.

There is no significant difference between neighborhood and well-being scores.

My neighborhood is significantly different from the state in terms of well-being scores.

The well-being scores in my neighborhood are significantly higher than the general well-being scores in the state.

Question 10 1 pts

The result regarding significance only tells us whether the difference between the two populations being compared is statistically significant, but it does not tell us how big the potential difference is. Calculate the standardized effect size for this test, using the information provided in the research scenario and the answers from previous questions. (Round the answer to 2 decimal places.)

Answer 1

DV-Level of well-being; IV-Location (state or my neighborhood)

Question 2 1 pts

Level of well-being in my neighborhood is not significantly different from the general level of well-being in my state.

Question 3 1 pts

From the data, mean of the sample is,

Mean () = (68 + 78 + 64 + 71 + 67 + 66 + 68 + 57 + 65 + 49 + 68 + 71 + 69 + 64 + 68 + 66) / 16 = 66.2

Question 4 1 pts

SE = = = 0.4

Question 5 1 pts

Z = ( - ) / SE = (66.2 - 65.5) / 0.4 = 1.75

Question 6 1 pts

Since we are interested in examining any difference between my sample and the population statistics not predicting or hypothesizing any particular direction of the difference, we use Two-tailed test.

Question 7 1 pts

For α = .05 and two-tailed test, the Z value is,

+1.96 and -1.96

Question 8 1 pts

Since the calculated Z statistic (1.75) is less than +1.96,

We fail to reject the null hypothesis because the calculated Z is less extreme than the critical Z value.

Question 9 1 pts

Since, we fail to reject the null hypothesis,

The well-being scores in my neighborhood are not significantly different from the well-being scores in the state.

Question 10 1 pts

Effect Size = ( - ) / = (66.2 - 65.5) / 1.6 = 0.44