Q1. Hypothesis Testing with a Z test (10 points total)

A research institute examined the IQs (intelligence quotients) in American adults and reported a mean () of 100 points and a standard deviation () of 15 points. But I wonder if the statistics in my city, Las Cruces, would be different from the national average. Specifically, I have a hunch that individuals in Las Cruces might have higher IQs compared to the national average.

To test this idea, I randomly picked 20 friends of mine living in Las Cruces and asked them their individual IQs. The data set is shown below. (The same data are also provided in an Excel file if you choose to use Excel for your calculations.)

I would like to perform a Z test to see if the IQs in Las Cruces (represented by the sample of 20 individuals) are significantly higher than the national average IQ. The significance level for my Z test was set at = .05. The hypotheses should be directional because I am predicting a specific direction of difference, and the test should be one-tailed.

Subject	IQ
1	93
2	109
3	94
4	98
5	99
6	128
7	92
8	106
9	114
10	118
11	122
12	94
13	115
14	109
15	87
16	110
17	92
18	108
19	86
20	95

Q1a. What is the dependent variable in this study? [1 point]

The dependent variable is the IQ

Q1b. What should be my null and alternative hypotheses? State each hypothesis using both words and statistical symbol notation. [2 points] 1 for each hypothesis: 0.5 for written, 0.5 for notation

	Written	Symbolic Symbol bank for copy & pasting: = < > m
Null		H0:
Alternative		H1:

Q1c. Calculate the sample mean. Round the result to the hundredth (2^nd place to the right of the decimal). [1 point] 0.5 if the process is correct but the result was calculated incorrectly

103.45, I added all of the IQs together and divided the number I got by the number of participants, 20.

Q1d. Calculate standard error using the population standard deviation given in the research scenario (SE, which is the standard deviation of the sampling distribution) Round the result to the hundredth (2^nd place to the right of the decimal). [1 point] deduct 0.5 if the process is correct but the result was calculated incorrectly

3.35, I took the standard deviation and divided by the square root of the sample size.

Q1e. Calculate the Z statistic (which indicates where our sample mean is located on the sampling distribution) Round the result to the hundredth (2^nd place to the right of the decimal). [1 point] deduct 0.5 if the process is correct but the result was calculated incorrectly

1.03, I got this by taking the sample mean, subtracting the national mean, 100, and dividing by the standard error. 103.45-100/3.35

Q1f. Determine the critical Z value(s). Explain how you find the answer. [1 point] 0.5 for the Z value, 0.5 for the rationale

Q1g. Compare the Z statistic with the appropriate critical Z value and then draw a conclusion about the result of the hypothesis test.

- Is the Z statistic more extreme than the critical Z? [0.5 point]

- Do you "reject" or "fail to reject" the null hypothesis? [0.5 point]

Q1h. Write a sentence to answer the research question (you can use the wording from the hypotheses or explain it in another way) [1 point]

Q1i. Calculate the standardized effect size Round the result to the hundredth (2^nd place to the right of the decimal). [1 point total] deduct 0.5 if the process is correct but the result was calculated incorrectly