Lab 3 – Binomial Distribution



Math 10 - Lab 3 Summer

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In this lab, we will create and interpret confidence intervals for means and proportions.

The BASIC STATISTICS>GRAPHICAL SUMMARY feature of MINITAB allows you to create confidence intervals for the population mean. You can set the confidence level to what you want.

Open the file RateMP.MPJ which represents the data from Rate my Professors that we have used in prior labs. For questions 2 to 4 you will need to use the "By Variables" option in MINITAB

1. Find a 95% confidence interval for the mean overall rating of instructors. Analyze and interpret the confidence interval. Determine the margin of error.

2. Find a 99% confidence interval for the mean overall rating of instructors. Analyze and interpret the confidence interval. Determine the margin of error. Compare your results to the question 6 and explain why the confidence interval has a higher margin of error.

3. Find 95% confidence intervals for the mean overall rating of instructors at each college. Compare the confidence intervals. Do they seem to be different?

4. Find 95% confidence intervals for the mean overall rating of instructors by hotness. Compare the confidence intervals. Do they seem to be different?

Confidence Intervals for proportions can be run in Minitab using the command

STAT>BASIC STATISTICS>1 PROPORTION.

5. Confidence Intervals for proportion by Gender

a. Find a 95% Confidence Interval for the proportion of male instructors. What is the Margin of Error?

b. Interpret this confidence Interval.

c. Would you support a claim that women are underrepresented at these colleges? Explain

You can use the command DATA>SUBSET WORKSHEET to look at an individual department, for example. We want create a worksheet of just Mathematics Instructors, so select Condition and set 'Dept'="Mathematics".

6. Find a 95% Confidence Interval for the proportion of male mathematics instructors.

a. Interpret this confidence Interval.

b. Would you support a claim that women are underrepresented in the Mathematics Departments at these two colleges? Explain

Open the file Housing.MPJ which represents data about home sales in California

7. You want to conduct a hypothesis test about the mean home prices in California using the housing data file: housing.mpj. At the 1% significance level, design the test the hypothesis that the mean housing price is over $850,000.

a. First create a dotplot for the price data and paste the results here. Does the value $850,000 seem to be at the center of the data, above the center of the data, or below the center of the data?

b. State the null and alternative hypotheses in words.

c. State the null and alternative hypotheses in population parameters.

d. What model are you choosing and what assumptions are needed? Do you think the skewness and high outlier are a problem in choosing this model?

e. Conduct the test at a significance level of 1%, using MINITAB command Stat>Basic Statistics>1 Population t-test. Make sure you choose options to set Ha. Paste the results here. All price data is in $thousands, so you would enter $850,000 as 850.

f. Do you reject or fail to reject Ho?

g. State your conclusion in the context of the problem.

h. Using the online power calculator, determine the power of the test if the population mean is really $900,000. Assume the standard deviation is $450,000. (Remember the data is entered in $ thousands)

i. Using the online power calculator, determine the sample size needed to have 95% power for the test.

8. For the housing data above, we want to support the claim that the percentage of homes in California with garages is over 60%. We are going to conduct a Hypothesis Test using a significance level of 10%

a. State the null and alternative hypotheses in words.

b. State the null and alternative hypotheses in population parameters.

c. Create a bar chart of garage and under Chart Option, click box to show y as a percentage. Does the bar graph support the claim that more than 60% of homes have garages?

d. What model are you choosing and what assumptions are needed?

e. Using the online power calculator, determine the power of the test if the population proportion under Ha is 0.65

f. Conduct the test at a significance level of 5%, using MINITAB command Stat>Basic Statistics>1 Proportion. Make sure you choose options to set Ha. Paste the results here.

g. Do you reject or fail to reject Ho?

h. State your conclusion in the context of the problem.

9. You want to conduct a hypothesis test about the standard deviation of home prices in California using the housing data file: housing.mpj. At the 5% significance level, design a test to support the claim that the standard deviation housing price is not $400,000.

a. State the null and alternative hypotheses in words.

b. State the null and alternative hypotheses in population parameters.

c. What model are you choosing and what assumptions are needed?

d. Conduct the test at a significance level of 5%, using MINITAB command Stat>Basic Statistics>1 Variance. Make sure you choose options to set Ha. Paste the results here.

e. Do you reject or fail to reject Ho?

f. State your conclusion in the context of the problem.

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