Question

A section of an Introduction to Psychology class took an exam under a set of unusual circumstances. The class took the exam in the usual classroom, but heavy construction noise was present throughout the exam. For all previous exams using the same format and same questions, student scores were normally distributed with a mean of �?�µ = 75.00 and a population standard deviation (sigma) = 10.50. To understand the possible effects of the construction noise, you have been asked to perform a number of statistical procedures for the following sample of exam scores obtained during the construction noise:

Construction Noise Exam Scores

57 58 59 60 61 64 65 66 66 67 67 68

68 69 69 70 70 70 70 71 72 72 72 72

72 73 75 77 78 81 82 83 84 88 96 100

What is the z score for a raw score of 70 in the POPULATION? Be sure to use the population calculation for a z-score.

What proportion of scores are above 70 in the population? (Note: This answer would be the same as if you answered what is the probability of randomly selecting a score greater than 70 from the population?)

In the population distribution, what raw score value is found at a z score of -3.00?

What is the standard error for the distribution of sample means when n = 36?

When n = 36, what is the z score that corresponds to the sample mean test score that was observed during the construction noise (the mean you computed in question #1)? ( Question one was just the mean of this equation :) )

When n = 36, what proportion of means in the distribution of sample means is less than the sample mean test score that was observed during the construction noise (the mean you computed in question #1)?( Question one was just the mean of this equation :) )

In the sampling distribution, what mean is found at a z score of -3.00?

Answer 1

population mean u =75

standard deviation sigma =10.5

sample mean X-bar = 72

and sample std s = 9.695

>> z-score = (x - u) / sigma

=(70 - 75) / 10.5

= - 0.476

>> Prob ( X > 70) = Prob ( Z > -0.476 )

= 1 - Prob ( Z <= -0.476 )

= 1 - 0.318 ( From standard normal table )

= 0.682

  

>> z-score = (x - u) / sigma

-3 = (x - 75) / 10.5

x = 43.5

>> s( X-bar) = s / root (n)

=9.695 / root (36)

= 1.6158

>> z-score = (x - x-bar) / s(x-bar)

= (72 - 72 ) / 1.6158

= 0

>>Prob ( X <= 72 ) = Prob ( Z< = 0 ) = 0.5 ) from standard normal table

>> z-score = (x - x-bar) / s(x-bar)

-3 = (x - 72) / 1.6158

x =67.152