# Test of hypothesis

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4. A neurologist wants to detect whether the mean response time for drug-injected rats differs from a control group not injected. The control group has the mean response time of 1.2 seconds. 100 rats are randomly chosen and injected with a unit dose of the drug. The average response time for the injected rats is 1.05 seconds with s = 0.5 seconds. Test the hypothesis at a level a= .01 whether there is a difference in response times.

5. A major car manufacturer wants to test a new engine to determine whether it meets new air-pollution standards. The mean emission m of all engines must be less than 20 parts per million of carbon. Ten engines are manufactured for testing purposes and the emission level of each is determined to be: 15.6 16.2 22.2 20.5 16.4 19.4 16.6 17.9 12.7 13.9. Does the data supply sufficient evidence to allow the manufacturer to conclude this type of engine meet the pollution standard? Test the hypothesis at a level a = 0.01.

6. The National Science foundation, in a survey of 2237 engineering graduate students who earned PhD degrees, found that 607 were US citizens; the majority (1630) of the PhD degrees were awarded to foreign nationals. Conduct a test to determine whether the true percentage of PhD degrees awarded to foreign nationals exceeds 50% at a level a = 0.01.

7. In the past decade intensive anti-smoking campaigns have been sponsored by both federal and private agencies. Suppose the American Cancer Society randomly samples 1500 adults in 1985 and then sampled 2000 adults in 1995 to determine whether there was evidence that the percentage of smokers had increased. The results of two independent surveys found that in 1985, out of 1500 surveyed, 576 were smokers. In 1995, out of 2000 surveyed, 652 were smokers. Does this data indicate that the proportion of smokers decreased over this 10 year period? Test at a level a=0.05.

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4. A neurologist wants to detect whether the mean response time for drug-injected rats differs from a control group not injected. The control group has the mean response time of 1.2 seconds. 100 rats are randomly chosen and injected with a unit dose of the drug. The average response time for the injected rats is 1.05 seconds with s = 0.5 seconds. Test the hypothesis at a level a= .01 whether there is a difference in response times.

Null Hypothesis: Ho: μ=1.2

Alternative Hypothesis: H1: μ≠1.2

Significance level=α= 0.01 or 1%

No of tails= 2

This is a 2 tailed test because we are looking for area in both the tails

Since sample size= 100 >= 30

we will use normal distribution

Z at the 0.01 level of significance 2 tailed test = 2.5758

Decision rule:

If Z value for the sample is less than -2.5758 or more than 2.5758

Reject the Null Hypothesis

Mean=μ= 1.2 seconds

Standard deviation =σ= 0.5 seconds

sample size=n= 100

σx=standard error of mean=σ/√n= 0.05 = ( 0.5 /√ 100)

sample mean= 1.05 seconds

z=(sample mean-μ)/σx= -3 =(1.05-1.2)/0.05

Since, Z value for the sample = -3 is less than Z critical= -2.5758

Reject The Null Hypothesis

At a level a= .01 there is a difference in response times

5. A major car manufacturer wants to test a new engine to determine whether it meets new air-pollution standards. The mean emission m of all engines must be less than 20 parts per million of carbon. Ten engines are manufactured for testing purposes and the emission level of each is determined to be: 15.6 16.2 22.2 20.5 16.4 19.4 16.6 17.9 12.7 13.9. Does the data supply sufficient evidence to allow the manufacturer to conclude this type of engine meet the pollution standard? Test the hypothesis at a level a = ...

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