Introduction to Hypothesis Testing (T)

7/27/2019 Introduction to Hypothesis Testing (T)

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PR2103

Pharmacostatistics

2013

Dr Perry Lim

Introduction toHypothesis Testing


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2

Q1: The mean lung capacity for non-smokers was reported to be

2 L. A random sample of 40 smokers has a mean lung capacity

of 1.8 L. is assumed to be 0.35 L. Is the lung capacity ofsmokers different from that of non-smokers at a significance level

of 5%?

35.0;2;8.1;40 0 xn ( is known)z-score

There is no difference between lung capacities of smokers and

non-smokers.

n

xz

0 61.3

4035.0

28.1

z

Lung capacity of smokers is different from that of non-smokers.

and are sample and population mean lung capacities of smokers.

0 is lung capacity of non-smokers.

x

H0: = 2 L

H1: 2 L


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Q1: The mean lung capacity for non-smokers was reported to be

2 L. A random sample of 40 smokers has a mean lung capacity

of 1.8 L. is assumed to be 0.35 L. Is the lung capacity ofsmokers different from that of non-smokers at a significance level

of 5%?

5% significance level; = 0.05

z/2 = z0.025 = 1.96

z = |3.61| > |1.96| RejectH0

Conclusion: At a significance level of 0.05, there is a difference

between the lung capacities of smokers and non-smokers.

Acceptanceregion

z1.961.96

Rejection region

3.61

Rejection region


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Q2:A consumer group is investigating a producer of diet meals

to examine if their pre-packaged meals do contain the advertised

protein amount of 6 oz in each package. Based on the followingdata, is there any evidence that the meals do not contain the

advertised protein amount at a significance level of 1%?

6.16.05.85.65.54.94.24.74.85.2

5.86.06.14.95.55.75.16.04.95.1

n

xx

1

)( 2

n

xxs

395.5x 552.0s


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Pre-packaged diet meals contain advertised protein amount.

90.4

20552.0

6395.5

t

552.0;6;395.5;20 0 sxn ( is not known) t-score

ns

xt 0

Pre-packaged diet meals do not contain advertised protein amount.

and are sample and population mean protein amounts in diet meals.0 is advertised protein amount in diet meals.x

H0: = 6 oz

H1: 6 oz


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1% significance level; = 0.01 df= n 1 = 19

t/2,df= t0.005,19 = 2.861

Acceptanceregion

Rejection region

t2.8612.861

Rejection region

4.90

t = |4.90| > |2.861| RejectH0

Conclusion: At a significance level of 0.01, the pre-packaged diet

meals do not contain the advertised amount of protein.


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Q3: The mean hospital stay following a particular surgical

procedure in 2007 was reported to be 7.1 days. A researcher

feels that the mean hospital stay in 2008 could be shorter. Arandom sample of 45 patients undergoing the same surgical

procedure in 2008 had a mean stay of 6.24 days with a standard

deviation of 3.01 days. Run the appropriate test at = 0.05.

01.3;1.7;24.6;45 0 sxn ( is not known) t-score

Mean hospital stay in 2008 is not shorter than that in 2007.

ns

x

t0

Mean hospital stay in 2008 is shorter than that in 2007.

92.14501.3

1.724.6

t

and are sample and population mean hospital stays in 2008.0 is mean hospital stay in 2007.x

H0: = 7.1 days

H1: < 7.1 days


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Q3: The mean hospital stay following a particular surgical

procedure in 2007 was reported to be 7.1 days. A researcher

feels that the mean hospital stay in 2008 could be shorter. Arandom sample of 45 patients undergoing the same surgical

procedure in 2008 had a mean stay of 6.24 days with a standard

deviation of 3.01 days. Run the appropriate test at = 0.05.

5% significance level; = 0.05

Acceptance

region

t1.681

Rejection region

1.92

t = |1.92| > |1.681| RejectH0

Conclusion: At a significance level of 0.05, mean hospital stay in

2008 is shorter than that in 2007.

df= n 1 = 44

t,df= t0.05,44 = 1.681


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Q4:A companys cookie recipe states the sugar coating on a

cookie to be 16.4 g. A sample of 28 cookies taken at random has

a mean sugar coating weight of 16.6 g with standard deviation of1.2 g. Is the sugar coated on the cookies more than the stated

amount at 95% confidence level?

Stated amount of sugar is coated on the cookies.

88.0

282.1

4.166.16

t

2.1;4.16;6.16;28 0

sxn ( is not known)

t-score

ns

xt 0

Sugar coated on the cookies is more than stated amount.

and are sample and population mean sugar coating weights.

0 is stated sugar coating weight.

x

H0: = 16.4 g

H1: > 16.4 g


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Q4:A companys cookie recipe states the sugar coating on a

cookie to be 16.4 g. A sample of 28 cookies taken at random has

a mean sugar coating weight of 16.6 g with standard deviation of1.2 g. Is the sugar coated on the cookies more than the stated

amount at 95% confidence level?

df= n 1 = 27

t,df= t0.05,27 = 1.703

Acceptanceregion

t1.703

Rejection region

0.88

t = 0.88 < 1.703 Fail to reject H0

Conclusion: At 95% confidence level, the stated amount of sugar is

coated on the cookies.

95% confidence level; = 0.05


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Q5:A certain supplier has always supplied goods that is 6%

defective. A random sample of 250 units of the goods supplied

recently is found to be 3% defective. Is there an improvement inthe quality of the goods supplied at 95% confidence level?

06.0;03.0;250 0 ppn

There is no improvement in quality of goods supplied.

npp

ppz

)1(

00

0

There is an improvement in quality of goods supplied.

00.2250)06.01(06.0

06.003.0

z

andp are sample and population defective proportions of recent

goods, andp0

is defective proportion of previous goods.

p

H0:p = 0.06

H1:p < 0.06


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Q5:A certain supplier has always supplied goods that is 6%

defective. A random sample of 250 units of the goods supplied

recently is found to be 3% defective. Is there an improvement inthe quality of the goods supplied at 95% confidence level?

z =

z0.05 = 1.645

Acceptance

region

z1.645

Rejection region

2.00

z = |2.00| > |1.645| Reject H0

Conclusion: At 95% confidence level, there is an improvement in

the quality of the goods supplied.

95% confidence level; = 0.05

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Introduction to Hypothesis Testing (T)