A step-by-step review.

See Excel Spreadsheet 11.2.10 Regression line basics

Learning, Statistics, and me

Consider the following problem:

The grade point averages for 12 randomly selected students are shown in the table below. Find the 99% confidence interval around the population mean, µ.

Solution:

Because this is a small sample, n < 30, use the t-distribution.

The Excel solution is: [Read more…] about Single-Sample, Small Sample, Confidence Interval for a Mean

Sometimes you are confronted with a deceptively simple-looking problem:

Construct the indicated confidence interval for the population mean, µ.

c = 0.90, x-bar = 16.2, s = 5.0, n = 75.

To solve it you need to carefully inspect the data you are given. You should notice two things. You are not given the population standard deviation, σ, and the n is > 30.

Depending upon the author of your stats book (and your instructor), you will choose either the normal distribution or the t-distribution to solve it. Some authors say if you do not know sigma, use the t-distribution. Many authors say if n > 30, it is OK to use the normal distribution with s being approximately equal to σ. [Read more…] about Single-sample, Large Sample Confidence Interval for a Mean

Consider the following problem statement:

An article in an online magazine states that 40% of home buyers found their real estate agent through referrals by a friend. However, a professor in a local college sampled 1000 home buyers and found that 426 chose an agent recommended by a friend.

Does the data refute the claim made by the magazine? Use a significance level of 0.02.

Solution:

- First, you should recognize that this is a test about a single proportion, not a mean or other statistic.
- The claim is that the proportion of home buyers who select their real estate agent based on the recommendation of a friend is 0.40. Therefore, the claim is p = 0.40.
- Since the claim contains an equality, =, it must be the null.
**Ho: p = 0.40**. - The alternative must be the complement,
**Ha: p****≠ 40**. - Remember the rule of thumb is that all hypothesis tests for proportions are z-tests. But you should confirm that you can use the normal distribution by checking that both n*p and n*q are greater than 5. Here n*p = 2000*0.40 = 800 and n*q = 2000*(1-0.40) = 1200. Both are > 5, there we can use the normal distribution.
- I recommend always sketching the situation described in the problem. Here we see that the sample count of 426 falls on the right side of the hypothesized mean of 400 for the population. Recall, the mean for a proportion is just the n*p or 0.4 * 1000. The standard deviation for a proportion is

[Read more…] about Single-sample Hypothesis Test for a Proportion

If you run into a problem, usually in an academic setting, where you only know the multiple coefficient of determination, R^{2}, and are asked to test to see if the beta coefficients are non-zero, you can do this easily using Excel. You could also do it in StatCrunch using the Data > Compute tool, but I find it tedious compared to just building the solution in Excel. And, you can save the Excel solution for later reuse if you label and name it in a smart way.

Consider this problem:

Researchers want to use an analysis of social media to forecast the number of viewers, and thus ad revenues, for new TV series. They collected data on the pilot episodes for 33 series. The data included the number of times per minute a series was mentioned in the 24 hours after the pilots aired. It also included an analysis of the sentiment index of the mentions, i.e. ratio of positive to negative mentions. R^{2} for the 1^{st} order regression model they produced is 0.937; R_{a}^{2} = 0.933.

Test the model to see if it might be useful in forecasting ad revenues for a new TV series.

Solution:

- A first-order model consists of terms for quantitative independent variables. Because we have two independent variables, the model will be of the form:

[Read more…] about Perform Hypothesis Test for a Regression Model, Given R Squared

When we do not know the population standard deviation sigma, σ, and the sample size, n, is less than 30, we use the t-test to evaluate a claim. Consider the following problem:

A scientist thinks the mean waste recycled by adults in the US is now more than one pound per person per day. In a random sample of 12 US adults, the mean waste recycled per day per person is 1.9 pounds with a standard deviation of 0.3 pounds. At a 10% significance level, does the sample data support the claim?

In statistics, it is always a good idea to sketch the situation described in the problem:

The sample mean is far to the right of the assumed population mean, µ = 1. [Read more…] about Single-sample t-test & Confidence Interval – Excel & StatCrunch

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