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Statistics Powerpoint

You will also develop a PowerPoint presentation for the newly hired scientists on these topics, and you have been asked to provide two real-life examples that you will

describe step-by-step. Your boss has asked you to include the following slides:

Slide 1: Title slide

Slide 2: Describes the two differences between independent and dependent samples

Slide 3: Provides an example of independent samples when testing a new drug

Slide 4: Shows how to set up a hypothesis test for two independent proportions: One to test whether they are equal and another one to test whether one proportion is

larger than the other

Slide 5: Shows the formula for the test statistic for two independent proportions and lists what each variable in the formula represents

Slide 6: Shows the formula for the margin of error (E) when doing a confidence interval on two proportions and explains what each variable stands for

Slide 7: Other than proportions, describes what other types of hypothesis tests can be done for two independent samples

Slide 8: Provides an example of dependent samples (also known as matched pairs) when testing a new drug. The two samples should be a before and after test with the

same group

Slide 9: Shows the t formula for the test statistic for matched pairs and explains what each variable represents

Slide 10: Show what a confidence interval for matched pairs would look like using only variables. Also, include the formula for the Margin of Error and state what each

variable represents

To show the formulas above, you may need to use the following variables which you can copy from here:

Statistics Module 5

You will also develop a PowerPoint presentation for the newly hired scientists on these topics, and you have been asked to provide two real-life examples that you will

describe step-by-step. Your boss has asked you to include the following slides:

Slide 1: Title slide

Slide 2: Describes the two differences between independent and dependent samples

Slide 3: Provides an example of independent samples when testing a new drug

Slide 4: Shows how to set up a hypothesis test for two independent proportions: One to test whether they are equal and another one to test whether one proportion is

larger than the other

Slide 5: Shows the formula for the test statistic for two independent proportions and lists what each variable in the formula represents

Slide 6: Shows the formula for the margin of error (E) when doing a confidence interval on two proportions and explains what each variable stands for

Slide 7: Other than proportions, describes what other types of hypothesis tests can be done for two independent samples

Slide 8: Provides an example of dependent samples (also known as matched pairs) when testing a new drug. The two samples should be a before and after test with the

same group

Slide 9: Shows the t formula for the test statistic for matched pairs and explains what each variable represents

Slide 10: Show what a confidence interval for matched pairs would look like using only variables. Also, include the formula for the Margin of Error and state what each

variable represents

To show the formulas above, you may need to use the following variables which you can copy from here:

Module 05 –

Hypothesis Tests Using Two Samples

Class Objectives:

Identify whether two samples are independent or dependent.

Compare the testing procedures for two sample tests.

Test hypothesis about two population parameters.

________________________________________

Module 05 – Part 1

Last week we took one sample to see if it supported our alternative hypothesis. This week we are going to increase to TWO samples and see if there is a significant

difference between them.

When would we use this?

Two samples are __________________________________ if the sample values from one population are not related to or somehow naturally paired or matched with the

sample values from the other population.

Example:

Two samples are _____________________________ (or consist of ______________________________________) if the sample values are somehow matched, where the

matching is based on some inherent relationship.

Example:

Hint: If the two samples have different sample sizes with no missing data, they must be independent. If the two samples have the same sample size, the samples may or

may not be independent.

Put the variables in for each population in the table below.

Population 1 Population 2

Population Mean

Population Standard Deviation

Population Proportion

Sample Size

Sample Mean

Sample Standard Deviation

Sample Proportion

Note: We are going to approach the problem as if σ_1 “and ” σ_2 are unknown. This is the most common and means that we will be using the t test statistic.

The test statistic is given by the formula below:

t=((x ̅_1-x ̅_2 )-(μ_1-μ_2))/√((s_1^2)/n_1 +(s_2^2)/n_2 )

where we assume μ_1-μ_2=0.

Degrees of freedom are either _________________________ or ________________________. Pick whichever sample size is smaller.

We will be doing the same steps as before to test the hypothesis (either critical value or p-value test). There are just different formulas.

The null hypothesis is given as _____________________________.

The alternative hypothesis will be either ____________________________, ___________________________, or _____________________________.

Example. Data Set 26 “Cola Weights and Volumes” in Appendix B includes weights (lb) of the contents of cans of Diet Coke (n = 36, x = 0.78479 lb, s = 0.00439 lb) and

of the contents of cans of regular Coke (n = 36, x = 0.81682 lb, s = 0.00751 lb). Use a 0.05 significance level to test the claim that the contents of cans of Diet

Coke have weights with a mean that is less than the mean for regular Coke.

Module 05 – Part 2

Inferential statistics involves forming conclusions about population parameters.

These population parameters could be:

The activities that we could perform on two samples are estimating the value of the population parameters using confidence intervals and testing claims made about the

population parameters.

Independent Samples Dependent Samples

Samples taken from two different populations, where the selection process for one sample is independent of the selection process for the other sample.

Samples taken from two populations where either (1) the element samples is a member of both populations or (2) the element samples in the second population is

selected because it is similar on all other characteristics, or “matched,” to the element selected from the first population.

Example.

Example.

Example.An educator is considering two different videotapes for use in a session designed to introduce students to the basics of economics. Students have been

randomly assigned to two groups, and they all take the same written examination after viewing the videotape. The scores are summarized below. Assuming normal

populations with unknown population standard deviations, does it appear that the two videos could be equally effective? Use a level of significance of 0.05.

Videotape 1: (x_1 ) ̅=77.1, s_1=7.8, n_1=25

Videotape 2: (x_2 ) ̅=80.0, s_1=8.1, n_1=25

The hypothesis Test for two dependent samples is a bit different because we need to use the difference from each matched pair to test the claim.

The test statistic for dependent samples uses the following formula:

t=(d ̅-μ_d)/(s_d/√n)

Example.Here we consider one aspect of how we treat women and men differently based on their ages. Data Set 14 “Oscar Winner Age” in Appendix B lists ages of actresses

when they won Oscars in the category of Best Actress, along with the ages of actors when they won Oscars in the category of Best Actor. The ages are matched according

to the year that the awards were presented. Table 9-2 includes a small random selection of the available data so that we can better illustrate the procedures of this

section. Use the sample data in Table 9-2 with a 0.05 significance level to test the claim that for the population of ages of Best Actresses and Best Actors, the

differences have a mean less than 0 (indicating that Best Actresses are generally younger than Best Actors).