# Statistics I Worksheet

### Description

Explanation & Answer length: 7 Questions

) All work (except where noted) should be calculated using StatCrunch. Include all required StatCrunch print-outs with your project.

1. Use the data from Chapter 2 (2.1 Exercise 40 – Triglyceride levels)

a) Create a Frequency and Relative Frequency distribution.

b) Create a Histogram.

c) State the modal class and state whether the distribution is symmetric, left-skewed, or right skewed.

d) Create a Stem-and-Leaf plot.

e) Create a Dot Plot.

f) Find the mean, median, range, standard deviation, variance, and IQR. g) Find the five number summary.

h) Create a Box Plot and identify any outliers.

2. A salesperson uses random digit dialing to call people and try to interest them in applying for a charge card for a large department store chain. From past experience, he is successful on 4% of his calls. On a typical working day he makes 180 calls. Let the random variable x be the number of calls on which he is successful. a) Use StatCrunch to find the probability that on a given day he has

i) Exactly 10 successful calls

ii) More than 10 successful calls Note: Include StatCrunch printouts

iii) Between 5 and 15 (inclusive) successful calls

iv) Less than 8 successful calls

b) Explain why the x-scale for this distribution does not extend out to 180.

c) Calculate, by hand, how many successful calls you would expect each day.

d) Calculate, by hand, the standard deviation of the variable X.

e) Based on our study of normal curves, would you be able to use the normal curve approximations for this distribution? Explain your answer.

3. Use the data from Chapter 6 (6.2 Exercise 32 – Annual Earnings (in dollars) of Intermediate Level Life Insurance Underwriters)

a) Check to see if the sample size / normality assumption is satisfied.

b) Construct a 99% confidence interval for the population mean annual earnings. (Include StatCrunch print-out.)

c) Interpret your confidence interval from part

d) Construct a 90% confidence interval for the population mean annual earnings. (Include StatCrunch print-out.)

4. In a survey of 2040 U.S. adults in a recent year, 650 made a New Year’s resolution to eat healthier.

a) Check to see if the sample size / normality assumption is satisfied.

b) Construct a 95% confidence interval for the population proportion of U.S. adults who made a New Year’s resolution to eat healthier. (Include StatCrunch print-out.)

c) Interpret your confidence interval from part (b) using percentages rounded to the tenths place.

d) Construct a 99% confidence interval for the population proportion of U.S. adults who made a New Year’s resolution to eat healthier. (Include StatCrunch print-out.)

5. Use the data from Chapter 7 (Chapter 7 Review Exercise 43 – scores for grade 12 students on a science achievement test). An education publication claims that the mean score for grade 12 students on a science achievement test is 140. You want to test this claim. You randomly select 36 grade 12 test scores. The results are in the data file (Chapter 7 Review Exercise 43). At the 5% significance level, do you have enough evidence to reject the researcher’s claim?

a) Create a histogram and boxplot for the sample data. Discuss normality, whether or not outliers are present, and sample size and how each of these may affect the validity of our results.

b) Using correct notation, state the null hypothesis.

c) Using correct notation, state the alternative hypothesis.

d) Use StatCrunch to calculate the p-value for this significance test. (Include StatCrunch printout.) e) At a 5% significance level, clearly state your resulting decision: “Reject H0” or “Do Not Reject H0.” f) Interpret your significance test results.

6. A research center claims that less than 24% of U.S. adults’ online food purchases are for snacks. In a random sample of 1850 U.S. adults, 22% say their online food purchases are for snacks. At the 1% significance level, is there enough evidence to support the center’s claim?

a) Using correct notation, state the null hypothesis.

b) Using correct notation, state the alternative hypothesis.

c) Use StatCrunch to calculate the p-value for this significance test. (Include StatCrunch printout.)

d) At a 1% significance level, clearly state your resulting decision: “Reject H0” or “Do Not Reject H0.”

e) Interpret your significance test results.

7. Use the data from Chapter 9 (9.2 Exercise 23 – caloric contents and sodium contents (in mg) of beef hot dogs).

a) Obtain a scatterplot using “calories” on the x-axis and “sodium” on the y-axis. (Include a StatCrunch print-out.)

b) Obtain the correlation coefficient. (Include a StatCrunch print-out.)

c) Discuss any association / relationship between these two variables (including strength of association and whether it is a positive or negative correlation).

d) State the prediction equation. (Include a StatCrunch print-out.)

e) Find the residual for the hot dog with 170 calories and 520 mg of sodium.

f) Use your prediction equation to predict the sodium content of a hotdog that is 120 calories. Round your answer to the tenths place and include units with your answer.

Mth 245 𝑥̅ = Test 1 ∑𝑥 Formula Sheet 𝑠𝑥 = √ 𝑛 ∑(𝑥−𝑥̅ )2 𝑛−1 Sample Variance = (𝑠𝑥 )2 IQR = 𝑄3 − 𝑄1 lower limit (fence) = 𝑄1 − 1.5 ∙ 𝐼𝑄𝑅 Chebychev’s Theorem: 𝑧= 𝑥−𝑥̅ 𝑘2 𝑧= 𝑥−𝜇 𝜎 𝑃(𝐴𝑐 ) = 1 − 𝑃(𝐴) General multiplication rule: Special multiplication rule: Conditional: 1 or 𝑠 Complements: 1− upper limit (fence) = 𝑄3 + 1.5 ∙ 𝐼𝑄𝑅 𝑃(𝐴 𝐵 ) = General addition rule: Special addition rule: 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 𝑃(𝐴) ∙ 𝑃(𝐵 𝐴) 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 𝑃(𝐴) ∙ 𝑃(𝐵) 𝑃(𝐴 𝑎𝑛𝑑 𝐵) 𝑃(𝐵) = 𝑛(𝐴 𝑎𝑛𝑑 𝐵) 𝑛(𝐵) 𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 𝑎𝑛𝑑 𝐵) 𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) Mth 245 Test 3 invNorm(A, µ, σ) Formula Sheet normalcdf(a, b, µ, σ) tcdf(a, b, df) invT(A, df) Significance Tests (One Sample) Proportion 𝑧 = Mean 𝑝̂−𝑝0 𝑧= 𝑠𝑒0 where 𝑠𝑒0 = √ 𝑥̅ −𝜇0 𝜎/√𝑛 𝑝𝑜 ∙(1−𝑝0 ) 𝑡= 𝑥̅ −𝜇0 𝑠/√𝑛 df = n – 1 𝑛 If 𝑝 ≤ 𝛼 Then Reject H0 Significance Tests (Difference Between Two Samples – Indep) (x̅1 − x̅2) – (μ1 – μ2) z = σ12 σ22 √n + n 1 2 Confidence Interval (Difference Between Two Samples – Indep) (𝑥̅1 − 𝑥̅2 ) − 𝑧𝑐 √ 𝜎12 𝑛1 + 𝜎2 2 < 𝜇1 − 𝜇2 < (𝑥̅1 − 𝑥̅2 ) + 𝑧𝑐 √ 𝑛2 𝜎1 2 𝑛1 + 𝜎2 2 𝑛2 Significance Tests (Difference Between Two Samples – Paired) 𝑑̅ − 𝜇𝑑 𝑡 = 𝑠𝑑 √𝑛 𝑤ℎ𝑒𝑟𝑒 𝑑̅ = ∑𝑑 𝑛 Confidence Interval (Difference Between Two Samples – Paired) 𝑑̅ − 𝑡𝑐 𝑠𝑑 √𝑛 < 𝜇𝑑 < 𝑑̅ + 𝑡𝑐 𝑠𝑑 √𝑛 Significance Tests (Presence of Correlation) 𝑡 = Residual: 𝑑 = 𝑦 − 𝑦̂ 𝑟 2 √1−𝑟 𝑛−2 df = n – 2

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