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MATH 3070: Quiz No.4
NAME:
Instruction. Print your name. In each question indicate your choice (when it is multiplechoice), or provide a short answer (probability/number/statistical terms, a few sentences).
Question 1. The chemistry lab manual says “your own experiment should conclude with
significance level 0.05 that the population mean is greater than 4.2. In the experiment you are
supposed to make 20 measurements, and use the critical region T 1.73 .”
1) Describe what null hypothesis should be in this experiment.
(a) T 1.73 ;
(b) T ≤ 1.73 ;
(c) the population mean is greater than 4.2;
(d) the population mean is less than or equal to 4.2.
2) Choose the correct statement regarding type I error.
(a) The data set has outliers;
(b) the null hypothesis is rejected when it is true;
(c) the null hypothesis is rejected when it is false;
(d) the null hypothesis is not rejected when it is false.
3) What does the lab manual intend to guarantee for the probability of Type I error?
(a) It is usually about 1%;
(b) it must be less than 5%;
(c) it must be less than 10%;
(d) we cannot guarantee anything about it.
4) Suppose that we obtain the test statistic T = 1.55 . What do you say about the null
hypothesis?
5) If T = 1.55 , what would you conclude in our lab report?
(a) The population mean is greater than 4.2;
(b) the population mean is less than 4.2;
(c) there is not sufficient evidence to support the claim of the lab manual;
(d) there is not sufficient evidence to support T 1.73 .
Question 2. A tobacco company has been claiming that the average nicotine content of their
product is at most 14mg per cigarette. A researcher tested 100 cigarettes for their nicotine
content. In this study he reported the sample mean 14.6mg, casting his doubt regarding the
company's claim.
6) Choose the alternative hypothesis the researcher should use for his hypothesis test.
(a) The mean nicotine content is equal to 14.6mg;
(b) the mean nicotine content is greater than 14mg;
(c) the mean nicotine content is equal to 14mg;
(d) the mean nicotine content is less than or equal to 14mg.
7) Besides the above description of his study what else do we need in order to calculate the
test statistic and the p-value.
(a) The assumption that the sample distribution is approximately normal;
(b) the sample standard deviation;
(c) the median;
(d) the significance level.
8) Suppose that we obtain the p-value 0.122. What can the researcher say about his doubt
regarding the company's claim?
9) Choose the correct statement regarding type II error.
(a) The probability that we correctly conclude that the alternative hypothesis is true;
(b) the probability that we correctly conclude that the null hypothesis is true;
(c) the probability that we incorrectly reject the null hypothesis when it is true;
(d) the probability that we incorrectly accept the null hypothesis when it is false.
10)
Suppose that the probability of type II error is larger than what the study requires.
What shall the researcher do?
(a) conclude that the company's claim is correct;
(b) conclude that further study is unnecessary;
(c) recommend to decrease the sample size in the future study;
(d) recommend to increase the sample size in the future study.