Question 12

Null Null Hypothesis Theoretical non-null value Any mean Type Il error Alternative Hypothesis HI Type I error

HYPOTHESIS TESTING OUTCOMES Reality The Null Hypothesis Is True Accurate Type I Error h The Null Hypthesis Is True The Alternative Hypothesis is True The Alternative Hypothesis is True Type Il Error Accurate O

Type I error, also known as a "false positive": the error of rejecting a null hypothesis when it is actually frue. In other words, this is the error of accepting an alternative hypothesis (the real hypothesis of interest) when the results can be attributed to chance. Plainly speaking, it occurs when we are observing a difference when in truth there is none (or more specifically - no statistically significant difference). So the probability of making a type I error in a test with rejection region R is P(R I Ho is true) . Type Il error, also known as a "false negative": the error of not rejecting a null hypothesis when the alternative hypothesis is the true state of nature. In other words, this is the error of failing to accept an alternative hypothesis when you don't have adequate power. Plainly speaking, it occurs when we are failing to observe a difference when in truth there is one. So the probability of making a type Il error in a test with rejection region R is 1 — P(R I Ha is true). The power of the test can be P(R IHa is true) .

Question 15

What Does 95% Confidence Mean Anyway? • A 95% confidence interval means that the method used to construct the interval will produce intervals containing the true p in about 95% of the intervals constructed. • This means that if the 95% Cl method was used in 100 different samples, we would expect that about 95 of the intervals would contain the true p, and about 5 intervals would not contain the true p. Spo kane Virtual Learning Excellence for Everyone. Fv.wwher, Everyday

Question 22

Sampling Distribution Variable Categorical (example: left-handed or not) Quantitative (example: age) Parameter P = population proportion g = population mean, o = population standard deviation Statistic D — sample proportion x = sample Center Spread PCI — p) Shape Normal IF np 10 and n(l -p) 10 When will the distribution of sample means be approximately normal

Question 23

  • 95% confidence interval of a sampling

    2% 3% 4% 5% Sample size = 2,401 Margin of error = 2% Sample size = 1,067 Margin of error = 3% Sample size = 600 Margin of error = 4% Sample size = 384 Margin of error = 5% Sample size = 96 Margin of error =10% 2,401 1,067 600 384 96

  • Margin of error vs. sample size at different confidence level

    Confidence Level Sample 150 200 250 350 450 500 550 600 650 700 750 850 900 950 1000 % Margin of % Margin of Error 5.3 3.0 2.9 2.7 2.2 2.0 Error 5.2 3.9 3.0 2.8 2.7 2.7 % Margin of 9.8 6.2 5.7 5.2 3.8

  • Equation

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Question 25

Standard error of difference • To compare two groups, we have to calculate the standard difference error between the 1- groups Distribution Parameter Population value Sample estimate Normal Binomial Poisson mean Proportion Rate Tt1-Tt2 PI-P2 Standard error -PI) P2(1-P2

Question 26

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Question 27

(row total) (column total) (grand total)

One rainy Saturday morning, Adam woke up to hear his mom complaining about the house being dirty. "Mom is always grouchy when it rains," Adam's brother said to him. So Adam decided to figure out if this statement was actually true- For the next year, he charted every time it rained and every time his mom was grouchy. What he found was very interesting - rainy days and his mom being grouchy were entirely independent events\_ Some of his data are shown in the table below. Fill in the missing values from the frequency table. Grouchy Not grouchy Column total Raining 35 Not reining 26 H 330 Row total 73 292 365 muc.Åv

Question 30

In engineering, science, and statistics, replication is the repetition of an experimental condition so that the variability associated with the phenomenon can be estimated. ASTM, in standard E1847, defines replication as "the repetition of the set of all the treatment combinations to be compared in an experiment. Replication (statistics) - Wikipedia https://en.wikipedia.org/Wiki/Replication\_(statistics)

Question 33

Inferences about the Slope: Confidence Interval Example Confidence Interval Estimate of the Slope: Excel Printout for Produce Stores Lower 95% Upper 95% Intercept 475.810926 2797.01853 X Variable 1.06249037 1.91077694 At 95% level of confidence the confidence interval for the slope is (1.062, 1.911). Does not include O. 0 20 Conclusion: There is a significant linear dependency annual sales on the size of the store. unap 1 U-4

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Question 38

"Blocking" vs "stratification" 'Blocking" • word used in describing an experimental design "Stratification" • used in describing a survey or observational study • Both refer to idea of only making comparisons within relatively similar groups of subjects Chapter 6 8

Question 40

  • Original data

    0.00 0.13 0.26 0.39 0.52 0.65 0.78 0.91

  • Sampling distribution of the sample mean with sample size = 2

    0.00 0.13 0.26 0.39 0.52 0.65 0.78 0.91

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