SOLUTION: SHOW THE COMPLETE SOLUTION AND THE SIX STEPS IN SOLVING THIS HYPOTHESIS TESTING The mean number of close friends for the population of people living in the U.S. is 5.7. The stan

Question 1182469: SHOW THE COMPLETE SOLUTION AND THE SIX STEPS IN SOLVING THIS HYPOTHESIS TESTING
The mean number of close friends for the population of people living in the U.S. is 5.7. The standard deviation of scores in this population is 1.3. An investigator predicts that the mean number of close friends for introverts will be significantly different from the mean of the population. The mean number of close friends for a sample of 36 introverts is 6.5. Do these data support the investigator's prediction? Use an alpha level of .05.
Thank you very much in advance!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
population mean is 5.7
population standard deviation is 1.3
test is for different, therefore two tailed confidence interval is indicated.
sample size is 36
sample mean is 6.5
test alpha = .05
this indicated a 95% confidence level.
with a two tailed test, half of the alpha is on the left of the distribution and half is on the right.
that indicates an alpha os .025
critical z-scores will be plus or minus 1.96
z-score formula is:
z = (x = m) / s
x is the mean of the sample.
m is the mean of the population.
s is the standard error.
s = psd / sqrt(ss) = 1.3 / sqrt(36) = .2167 rounded to 4 decimal places.
psd = population standard deviation
ss = sample size
z-score formula becomes:
z = (6.5 - 5.7) / .2167 = 3.69 rounded to 2 decimal places.
that is significantly higher than the critical z-score, indicating that the results of the test are significant.
significant results mean that the evidence suggest that the mean of the introverts is different from the mean of the popuation at large.

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