# 3 Statistics Problems

1. Which hypothesis testing model would be used under each of the following conditions. Use the "model number" from my handout if you wish. By line the information given in each cell is: Level of measurement, number of groups, sample size to be taken, parameter of interest and any qualifications.

[Please refer to the attachment for the Table].

2. Prove that a population mean is not equal to 150. Use an alpha of 5% and set up the full, detailed, five step hypothesis test. Assume when the sample 201 is taken the sample mean is 151.77 and the sample standard deviation is 10.

Use full 5-step formal hypothesis testing structure.

Estimate the p value?

3. Test to see if four population means are the same or different. Assume the populations are normally distributed and have equal variances. Use the formal hypothesis-testing model. State the conclusion in statistical terms and in conversational English. Use the ANOVA table below. Determine what the F-critical value is using an alpha of 5%.

[Please refer to the attachment for the Table].

#### Solution Preview

Please refer to the attachment.

Which hypothesis testing model would be used under each of the following conditions? Use the "model number" from my handout if you wish. By line the information given in each cell is: Level of measurement, number of groups, sample size to be taken, parameter of interest and any qualifications.

Conditions Model

Ratio data

One group

Large sample

Population mean

Don't know sigma

If Sample Size, n >= 30: One-sample z-test for the mean

If Sample Size, n < 30: One-sample t-test for the mean

Ratio data

Two groups

Large sample

Population means

Populations are normally distributed

Don't know sigmas but assume they are equal

Two sample t-test for the mean assuming unequal variances

Ratio data

Two groups

Large sample

Test for proportions

Two sample t-test for the mean assuming equal variances

Ratio data

Four groups

Large sample

Test for equality/inequality of means

ANOVA

I want to prove that a population mean is not 150. Use an alpha of 5% and set up the ...

#### Solution Summary

This solution is comprised of detailed step-by-step calculations and analysis of the given problems related to Statistics and provides students with a clear perspective of the underlying concepts.