Want to find if students who are musicians have higher Iq test scores than the general population. the researcher predicts that playing music is associated with higher IQ scores. the researcher selects a sample of 75 musicians from area and gives them an IQ test. The mean for the sample is 105. The mean for the general population is 100 with a standard deviation of 15. What is Z obt for this sample?
Z-statistic = (sample mean - population mean)/(standard deviation/square root of sample size)
sample mean = 105
population mean = 100
standard deviation = 15
sample size = 75
I'll let you take it from here to calculate.
To find the Z-score, you need to determine the difference between the sample mean and the population mean in terms of standard deviations.
The formula for calculating the Z-score is:
Z = (X - μ) / σ
Where:
Z is the Z-score
X is the sample mean
μ is the population mean
σ is the population standard deviation
In this case:
X (sample mean) = 105
μ (population mean) = 100
σ (population standard deviation) = 15
Now you can plug these values into the formula and calculate the Z-score:
Z = (105 - 100) / 15
Z = 5 / 15
Z = 0.3333 (rounded to four decimal places)
So the Z-score for this sample is approximately 0.3333.