Hypothesis Testing Please answer as soon as possible Show your steps and follow

Question

Hypothesis Testing

Please answer as soon as possible

Show your steps and follow the instructions for a good rate

****** Compute final answer using R (RStudio) ******

For each of the following problems, set up and perform the required hypothesis test. If the level of significance is not indicated, use ? = 0.05.

1. A claim is made by a laid-off employee in Silicon Valley that there is age discrimination by Silicon Valley tech companies. According to the US census, 30% of the adult population in Silicon Valley is between the ages of 40 and 65. In a random sample of 2100 adults employed at tech companies, 43 were between the ages of 40 and 65. Based on this sample, can we refute the employee’s claim that there is age discrimination? Use a significance level of 0.10.

2. The lapping process used to grind certain silicon wafers to the proper thickness is acceptable only if the population standard deviation of the thickness of dice cut from the wafers is less than 0.45 mil. A technician randomly chooses 17 dice cut from such wafers, computes that their standard deviation is 0.68 mil, and so claims that the process will fail. Test the technician’s claim. You may assume that in the population the wafer thicknesses are normally distributed.

Explanation / Answer

# Q 1.

## R command

n1= 2100 # sample size
X=40 # number of adults employed 43 were between the ages of 40 and 65
p=X/n1 # sample proportion
P=0.30 # population propertion of adults employed 43 were between the ages of 40 and 65

S.E=sqrt(P*(1-P)/n1) # standard error of

# Hypothesis

# Ho: P=0.30 VS H1: P does not equal to 0.30

t=(p-P)/S.E # test statistic
t
p.value=2*pt(q=t, df=209, lower.tail = TRUE)
p.value
## End

# Run

> n1= 2100 # sample size
> X=40 # number of adults employed 43 were between the ages of 40 and 65
> p=X/n1 # sample proportion
> P=0.30 # population propertion of adults employed 43 were between the ages of 40 and 65
>
> S.E=sqrt(P*(1-P)/n1) # standard error of
>
> # Hypothesis
>
> # Ho: P=0.30 VS H1: P does not equal to 0.30
>
> t=(p-P)/S.E # test statistic
> t
[1] -28.09524
> p.value=2*pt(q=t, df=209, lower.tail = TRUE)
> p.value
[1] 6.64337e-73

# End

Comment: The estimated p-value is less than 0.10 level of significance. Hence, we can reject the null hypothesis and conclude that there is age discrimination.

# Q 2.

## R command

n2=17 # sample size

s=0.68 # sample standard deviatiom
sigma=0.45 # population standard deviation

# Ho: sigma=0.45 VS H1: sigma < 0.45

# Test statistic

Chi.squrae=(n2-1)*(s/sigma)^2
Chi.squrae

##
p.value=pchisq(q=Chi.squrae, df=16, lower.tail = F)

p.value

# End

## Run

> n2=17 # sample size
>
> s=0.68 # sample standard deviatiom
> sigma=0.45 # population standard deviation
>
> # Ho: sigma=0.45 VS H1: sigma < 0.45
>
> # Test statistic
>
> Chi.squrae=(n2-1)*(s/sigma)^2
> Chi.squrae
[1] 36.53531
>
> ##
> p.value=pchisq(q=Chi.squrae, df=16, lower.tail = F)
>
> p.value
[1] 0.002436787

##

Comment: The estimated p-value is less than 0.05. Hence, we can not assume that in the population the wafer thicknesses are normally distributed at 0.05 level of significance.

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.