Assignment 2 Hypothesis Test One-Sample Test 11-10-2014 MGT 202

Answer the questions:a) Is this a one- or-two tailed test?b) What is the decision rule?c) What is the value of test statistic?d) What is your decision regarding HN?e) What is the p-value? Interpret it.

1. The following information is available. HN : µ =50

HA : µ ¿ 50A sample size is 36 provided a sample mean isΧ̄ 0f 49. The population standard deviation σ=5. Use the 0.05 significance level.

µ is knownPopulation Mean:0.05Significance Level:σ= 5Population standard deviation:

n= 36Sample Size:

x̄ = 49Sample Mean: a. two tailed test .b. Two tailed Z-test with α=0.05

Zα/2 = 1.96 Rejected H0 if z<-1.96 or z > 1.96 otherwise don't reject .

c. Test statistic

Z= x̄−µ0σ x̄

σ x̄ = σ√n =

5√36 = 0.833

Z=49−500.833 = -1.2

d. Decision and result:-Z= -1.2 > -1.96 Don't reject H0 No, we can't say that µ is different from 50

2. The following information is available. HN : µ¿ 10

HA : µ ¿ 10The sample mean isΧ̄ 12 for a sample of 36.The population standard deviation is 3. The population standard deviation σ=5. Use the 0.05 significance level. Use the 0.02 significance level.

µ is knownPopulation Mean:0.02Significance Level:σ= 3Population standard deviation:

n= 36Sample Size:x̄ = 12Sample Mean:

a. one tailed test .b. one tailed Z-test with α=0.02

Zα/2 = 0.5 – 0.02 = 0.48 look in table = 2.06Rejected H0 if z >2.06 otherwise don't reject .

c. Test statistic

Z= x̄−µ0σ x̄

σ x̄ = σ√n =

3√36 = 0.5

Z=12−100.5 = 4

d. Decision and result:-Z= 4 > 2.06 reject H0 yes, the mean is more than 10

3. The following information is available. HN : µ¿ 220

HA : µ ¿ 220

Steps of Hypothesis Testing: for ONE –Tailed Hypothesis

R.R = 4

0.5 – 0.02 = 0.48

a) Calculate z-value Ζ= Χ̄−μ

σ /√nb) Search for z-value from z-distribution tablec) Find ρ−value using: 0.5000- z-distribution value.d) Compare ρ−value with C.V.( α= 0.05 or 0.02 or 0.01….)e) Using decision Rule ( conclusion) as:

If ρ−value¿ α-value. Reject HN and

Accept HA . If ρ−value¿ α-value. Accept HN and

Reject HA .

4. Consider the following hypothesis test: HN : µ¿ 25

HA : µ ¿ 25

A sample of 100 is used and the population standard deviation is assumed to be 12. Use α= 0.05. Provide the value of the test statistic z and your conclusion for each of the following sample results:

a) Χ̄ =23.5

µ is knownPopulation Mean:0.05Significance Level:

σ= 12Population standard deviation:n= 100Sample Size:x̄ = 23.5Sample Mean:

one tailed test .

one tailed Z-test with α=0.02

Zα/2 = 0.5 – 0.05 = 0.45 look in table = 0.2088Rejected H0 if z > 0.2088 otherwise don't reject .

e. Test statistic

Z= x̄−µ0σ x̄

σ x̄ = σ√n =

12√100 = 1.2

Z=23.5−251.2 = -1.25

f. Decision and result:-Z= -1.21 < 2.088Don’t reject H0 no, the mean is less than 50

Steps of Hypothesis Testing: for ONE –Tailed Hypothesis

a) Calculate z-value Ζ= Χ̄−μ

σ /√nb) Search for z-value from z-distribution tablec) Find Pr ob . ability−value using: 0.5000- z-distribution value.d) Compare Pr ob . ability−value with C.V.( α= 0.05 or 0.02 or

0.01….)e) Using decision Rule ( conclusion) as:

If Pr ob . ability−value¿ α-value(0.05). Reject HN and

Accept HA . If Pr ob . ability−value¿ α-value. Accept HN and

Reject HA .

Q: MULTIPLE CHOICE QUESTIONS

In hypothesis testing, if the null hypothesis is rejected,a. no conclusions can be drawn from the testb. the alternative hypothesis is true*c. the data must have been accumulated incorrectlyd. the sample size has been too small

3. The level of significance is thea. maximum allowable probability of Type II errorb. maximum allowable probability of Type I error*c. same as the confidence coefficientd. same as the p-value

A Type II error is committed whena. a true alternative hypothesis is mistakenly rejected*b. a true null hypothesis is mistakenly rejectedc. the sample size has been too smalld. not enough information has been available

6. The error of rejecting a true null hypothesis isa. a Type I error*b. a Type II errorc. is the same as d. committed when not enough information is available

7. The level of significance in hypothesis testing is the probability ofa. accepting a true null hypothesisb. accepting a false null hypothesisc. rejecting a true null hypothesis *d. None of these alternatives is correct.

8. The level of significancea. can be any positive valueb. can be any valuec. is (1 - confidence level) *d. can be any value bet ween -1.96 to 1.96

8. From the information summarized in the following diagram:

The ρ-Value in the shadowed area is:a) 0.0179b) 0.0117c) 0.0021d) 0.9821 *