Hypothesis Scenario Assignment Report

STATISTICS
STUDENT ID:
[Pick the date]

Problem 1.03
(1) The appropriate hypothesis test for the given scenario is one sample Z test for proportion.
This is because there is only sample whose proportion ought to be tested. The underlying
binomial distribution for the variable can be approximated into normal distribution
thereby implying z statistic as the appropriate test statistic.
(2) Hypothesis Testing
Step 1: Hypotheses
Null hypothesis H0 : P=0.75
Alternative hypothesis Ha : P>0.75
Step 2: The test statistics
p= 237
300 =0.79
z stat = p−P
√ P ( 1−P )
n
= 0.79−0.75
√ 0.75 ( 1−0.75 )
300
=1.6
z stat =1.60
Step 3: Significance level
Significance level = 0.05
Step 4: The p value
The p value for the computed z stat.
The p value = 0.00
Step 5: Result
The p value does not exceed significance level i.e. 0.00< 0.05 and thus, rejection would be
done for null hypothesis. As a result of this, alternative hypothesis will be accepted.
Step 6: Conclusion
The final conclusion can be drawn that more than 75% of students of TRU derive to the
campus.
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Problem 1.04
(1) The appropriate hypothesis test is one sample t test because the population standard
deviation is not given which means Z test cannot be used here. Also, there is one variable
of interest thereby implying one sample test.
(2) Hypothesis Testing
Step 1: Hypotheses
Null hypothesis H0 :μ=10
Alternative hypothesis Ha : μ>10
Step 2: The test statistics
t= ( x−μ )
σ
√n
t stat= 11−10
3
√ 30
t stat=1.8257
Step 3: Significance level
Significance level = 0.05
Step 4: The p value
Degree of freedom = Sample size – 1 = 30 -1 = 29
The p value for the computed t stat and degree of freedom.
The p value = 0.0391
Step 5: Result
The p value does exceed significance level and thus, sufficient evidence is existed to say that
rejection would be done for null hypothesis. As a result, there is acceptance of alternative
hypothesis.
Step 6: Conclusion
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