Homework: pg. 727 & 738 49.) A. Ho: p=0.75, Ha:p>0.75 Type I Error: The manager decided that they were responding to more than 75% of the calls, when in fact they were responding is 75%. Type II Error: The manager decided that they were responding to 75% of the calls, when in fact they were responding to more than 75% in that time. Type I consequence: they may see no reason to improve, when in fact they should. Type II error consequence: officials try and make the response times faster when there is no need. Type I error, lives may be at stake Answers can vary, but most likely care more about mean response time

50.) A. Ho:µ=130; Ha:µ>130 B.) Type I Error: telling an employee that he has high blood pressure when in fact he does not. Type II Error: failing to notify an employee who has high blood pressure. You would want to decrease type II error because it is more serious. 52.) A. Ho:µ=10,000; Ha:µ<10,000 Type I Error: telling the consumer that the wood is weaker when in fact it is not; Type II Error: not telling the consumer that the wood is weaker when in fact it is Type II Error

69.) Ho:µ=150; Ha:µ<150 states random and Normal, Assume there is more than 2690 first year college students z=-3.28; P-value=0.0005, NEED SKETCH We reject the null hypothesis. If the avg. time of studying was 150 minutes, then the probability we got a sample mean of 137 is .05%. We have strong evidence to suggest that the students study less than 2.5 hours a night

Type I and Type II Errors And Power of a Test Section 11.4

Type I Error Rejecting the Null when it is actually true

Type II Error Failing to reject the Null when it is actually false

Power 𝑃𝑜𝑤𝑒𝑟=1−𝛽 (𝛽=𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑇𝑦𝑝𝑒 𝐼𝐼 𝑒𝑟𝑟𝑜𝑟) The probability that a test (with a fixed significance level) will reject the Null Hypothesis when a particular alternative value of the parameter is true Power = probability we correctly reject the null 𝑃𝑜𝑤𝑒𝑟=1−𝛽 (𝛽=𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑇𝑦𝑝𝑒 𝐼𝐼 𝑒𝑟𝑟𝑜𝑟)

Ways to increase Power (Decrease Type II Error) Increase α (Significance level) **This increases the probability of Type I Error * Sig Level = probability of Type I Decrease σ **Unless you can change your population, this is a set number. Increase sample size

Pg. 727 #49 Another way for the city manager to measure response times is to look at the proportion of calls for which paramedics arrived within 8 minutes. Last year, paramedics arrived on scene 75% of the time within 8 minutes. The city manager wants to determine whether they have done significantly better this year. State null and alternative hypotheses Describe a Type I and Type II error in this setting and explain the consequences of each. Which is more serious in this case?

Pg. 731 #54 The mean salt content of a certain type of potato chip is supposed to be 2.0 mg. The salt content of these chips varies Normally with a standard deviation σ=0.1 mg. From each batch produced, an inspector takes a sample of 50 chips and measures the salt content of each chip. The inspector rejects the entire batch if the sample mean salt content is significantly different from 2 mg at the 5% significance level.

A. )What null and alternative hypotheses is the inspector testing A.)What null and alternative hypotheses is the inspector testing? Define your parameter. B.) Explain what a Type I error would mean in this setting. What is the probability of making a Type I error? C.) Explain what a Type II error would mean in this setting. Find the probability of a Type II error if μ=2.05. D.) What is the power of the test to detect μ=2.05?

E. ) What is the power of the test to detect μ=1. 95 given 𝛽=. 0576. F E.) What is the power of the test to detect μ=1.95 given 𝛽=.0576? F.) If the inspector used a 10% significance level instead of a 5% significance level, how would this affect the probability of Type I error? A Type II error? The power of the test? G.) Would you recommend a 1%, 5%, or 10% significance level to the company? Justify your answer.

Homework Pg 727: #50, 52 Pg. 739: #73