STAT 111 Lecture Notes - Lecture 14: Null Hypothesis

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marooncrow273

23 Mar 2019

School

University of Vermont

Department

Statistics

Course

STAT 111

Professor

Jacob William Martin

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Document Summary

Type 1 error = rejecting a true null hypothesis (false positive) Type 2 error = not rejecting a false null hypothesis (false negative) The probability of making a type 1 error (rejecting a true null) is the significance level, [a] Because the chance of getting a type 1 error is [a], [a] of all tests with true null hypotheses will yield significant results just by chance. If 100 tests are done with a = 0. 05 and nothing is really going on, 5% of them will yield significant results, just by chance. Could be making a type 1 error if ho is true. Could be making a type 2 error if ha is true. If type 1 error is very bad, decrease the significance level. If type 2 error is very bad, increase the significance level. Larger sample size makes it easier to reject ho.

Related Questions

1.) Which of the following answers represents the objective of a hypothesis test?

a. Rejecting the null hypothesis when it is true.

b. Rejecting the null hypothesis when it is false.

c. Not rejecting the null hypothesis when it is true.

d. Rejecting the null hypothesis when it is false and not rejecting the null hypothesis when it is true.

2.) If the chosen significance level is ? = 0.05, then

a. there is a 5% probability of rejecting a true null hypothesis

b. there is a 5% probability of accepting a true null hypothesis

c. there is a 5% probability of rejecting a false null hypothesis

d. there is a 5% probability of accepting a false null hypothesis

browntoad1

Use the following scenario for questions 6 – 8. In 2016-17, the average SAT score of the UVA first year class was 1420 out of 1600. An advisor in the statistics department is interested in determining whether statistics majors from that class have higher SAT scores than the average. He tests H,:µ = 1420 against Hạ: µ > 1420, where u is the mean SAT score for statistics majors from the 2016-17 first year class. In a simple random sample of 30 statistics majors, he finds a sample mean SAT score of 1440 with sample standard deviation of 40.

6. What is the value of the test statistic for this significance test?

a. 0.09

b. 0.5

c. 2.73

d. 20

7. From what distribution is this test statistic?

a. N(0, 1)

b. N(1420, 7.30)

c. t distribution with 29 degrees of freedom

d. t distribution with 28 degrees of freedom

8.) The p-value for this test is 0.005. Which of the following is a proper interpretation of this p- value?

a.There is a 0.5% chance that the null hypothesis is true.

b. If the population mean SAT score really is 1420, there's a 0.5% chance that the sample a. mean SAT score from 30 statistics majors would equal 1440.

c.If the population mean SAT score really is 1420, there's a 0.5% chance that the sample mean SAT score from 30 statistics majors would be 1440 or lower.

d. If the population mean SAT score really is 1420, there's a 0.5% chance that the sample mean SAT score from 30 statistics majors would be 1440 or higher.

beigeserval271

One marketing strategy used by several companies is to send personalized emails or newsletters to their customers to encourage them to buy their product. However, the opening rate of these emails is very low when the targeted customers do not feel concerned by the email. This article 1 (https://www.crop.ca/en/blog/2019/258/) will allow us to answer the following questions. Here’s an excerpt from the article :

« A quick Google search for email and newsletter opening rates leads to dozens of sources, with rates ranging from 15% to 45%. Some even claim that opening rates higher than 25% are a resounding success. But seriously, can brands afford such poor performances ? And most importantly, why are opening rates so low ?

We asked the main stakeholders : consumers. 2,189 Canadians were ques- tioned about their attitudes and behaviours regarding branded newsletters and emails. The results follow. Of all branded communications received personally, Canadians report an average opening rate of 45%. »

(a) Do the results from the survey in the article in reference allow us to affirm that on average, Canadian consumers open more than 25 % of business communications sent by email and newsletters ? Suppose that the standard deviation in the population is 20 %. Use a significance level of α = 0, 05.

(b) From what average sample rate do we reject the null hypothesis of the test carried out in (a) ?

maroonraccoon733

STAT 111 Lecture Notes - Lecture 14: Null Hypothesis

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