A survey of 38 people was conducted to compare their self-reported height to their actual height. The difference between reported height and actual height was calculated.
You're testing the claim that the mean difference is greater than 0.8.
From the sample, the mean difference was 1, with a standard deviation of 0.52.
Calculate the test statistic, rounded to two decimal places
Z = (score-mean)/SEm
SEm = SD/√n
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
To calculate the test statistic, you can use the formula for the z-score:
Z = (X - μ) / (σ / √n)
Where:
X = Sample mean
μ = Hypothesized population mean
σ = Population standard deviation (or sample standard deviation)
n = Sample size
In this case, we are testing the claim that the mean difference is greater than 0.8. So, our null hypothesis (H0) would be:
H0: μ <= 0.8
And our alternative hypothesis (Ha) would be:
Ha: μ > 0.8
Given the sample mean difference of 1, the hypothesized population mean difference of 0.8, the sample standard deviation of 0.52, and the sample size of 38, we can plug these values into the formula to calculate the test statistic:
Z = (1 - 0.8) / (0.52 / √38)
Calculating the values inside the brackets first:
Z = 0.2 / (0.52 / √38)
Next, calculating the value inside the square root:
Z = 0.2 / (0.52 / 6.16)
Now dividing 0.2 by (0.52 / 6.16):
Z ≈ 0.2 / 0.084
Finally:
Z ≈ 2.38
Therefore, the test statistic, rounded to two decimal places, is Z = 2.38.