# hypothesis testing

**Topics:**Arithmetic mean, Statistical hypothesis testing, Standard deviation

**Pages:**5 (1203 words)

**Published:**May 9, 2014

Submission date: 9 May 2014

TUTORIAL ON HYPOTHESIS TESTING (1)

Basic Concept

1. State the null and alternative hypothesis for each conjecture : a. A researcher thinks that if expectant mothers use vitamin pills, the birth weight of the babies will increase. The average birth weight of the population is 3.0kg. b. An engineer hypothesizes that the mean number of defects can be decreased in a manufacturing process of compact disks by using robots instead of humans for certain tasks. The mean number of defective disks per 1000 is 8. c. A psychologist feels that playing soft music during a test will change the results of the test. The psychologist is not sure whether the grades will be higher or lower. In the past, the mean score was 73. d. The average time to read a certain passage is 15 minutes. An educator claimed that a course in speed reading will shorten the reading time. e. A chemist said that he invested an additive which can increase the life of batter. The mean lifetime is 24 months. f. The mean waiting bus for buses in Klang Valley is 8 minutes. Some roads are restricted to buses only during office hours. A test is performed to see how this has affected the mean waiting time.

2. Determine whether the one-tailed test or two-tailed test is appropriate for the situation given below: a. Testing whether the newly-purposed highway speed limit increases the number of accidents. b. Testing whether the mean weight of chicken changed by breeding with other brand of chicken feed. c. A manufacturer of brake cables tests to see whether the breaking strength is increased with implementing new technology in manufacturing process d. A manufacturer of ball-bearings tests to see whether the diameters are correct

3. Find the critical value(s) for each situation below and draw the appropriate figure, showing the critical region. a. A left-tailed test with α=0.10.

b. A two-tailed test with α=0.02.

c. A right-tailed with α=0.005.

d. α=0.05, two-tailed test.

e. α=0.10, left-tailed test.

f. α=0.01, right tailed test.

g. α=0.02, left-tailed test.

h. α=0.01, two-tailed test.

TOPIC : Testing the mean of a population

Case 1: Testing the mean of a population X where the variance is KNOWN (any sample size, n) The test statistic is: 4. Using normal distribution table, test the following hypotheses in each case:

Hypotheses

α

n

(a)

H0 : μ = 15.8

H1 : μ ≠ 15.8

15.2

3

0.05

30

(b)

H0 : μ = 26.3

H1 : μ > 26.3

27

1.2

0.05

10

(c)

H0 : μ = 123.5

H1 : μ > 123.5

125

4.2

0.01

49

(d)

H0 : μ = 4.4

H1 : μ < 4.4

4.35

0.18

0.02

100

3. A teacher claims that students in Class A put in more hours studying compared to other students. The mean numbers of hours spent studying per week is 25 hours with a standard deviation of 3 hours per week. A sample of 27 Class A students was selected at random and the mean number of hours spent studying per week was found to be 26 hours. Can the teacher’s claim be accepted at 5% significance level? 4.Trying to encourage people to stop driving to campus, the university claims that on average it takes people 30 minutes to ﬁnd a parking space on campus. I don’t think it takes too long to ﬁnd a spot. In fact, I have a sample of the last ﬁve times I drove to campus, and I calculated = 20. Assuming that the time it takes to ﬁnd a parking spot is normal, and that = 6 minutes, then perform a hypothesis test with level set α=0.10 to see if my claim is correct. 5.The packaging on a light bulb states that the bulb will last 500 hours under normal use. A consumer advocate would like to know if the mean lifetime of a bulb is less than 500 hours (a claim regarding the population mean). A random sample of n=49 light bulbs is burned to determine how long a light bulb lasts. Assume we know the...

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