Problem 1:

Below are five (5) separate distributions.

a. Calculate the Range

b. Use the range to calculate the standard deviation

c. Calculate the standard deviation (and show any difference)

Problem 2:

Two (2) students took the same statistics test.

Convert their scores to percentiles and plot on a chart.

You will need the z-table in the back of the text (or internet search).

Math Test Results

X = 73.0

s = 8.0

John scores 79 on the test

Mary scored 68 on the test

Problem 3:

I have finished analyzing the data from a recent study.

There are 25 subjects in the sample

The mean of the sample is 75

The standard deviation is 4.7

Please answer the following:

a. What is the standard error o the mean for these data?

b. What are the 95% and 99% confidence intervals

c. What is the probability of obtaining by chance the following:

i. a mean less than 72

ii. a mean less than 74

iii. a mean greater than 76

iv. a mean greater than 78

Problem 4

Use the following information to write the correspondingnull and alternative hypothesis:

a. A sample mean of 23 is statistically different from a population mean of 30

b. A sample mean of 56 is less than the population mean of 70

c. A sample mean of 75 is greater than the population mean of 70

Be sure to show the relationship! Not just words.

Problem 5

I am back in the lab, collecting samples.

The mean of the sample is 75

My associate wants to determine whether the sample meanstatistically greater than the population mean of 70.

My associate set α = 0.05

Please provide responses to:

a. The probability associated with a mean of 75 is p = 0.05Can my associate reject the null hypothesis?

b. If the null hypothesis is a correct statement, what is the probability that the researcher will make the correct decision not to reject the null hypothesis?