Null/Alternative hypothesis, Test Statistics, P-Value, Conclusion

Question

1.
Listed below are the number of years it took for a random sample of college students to earn a bachelor's degree. At the .05 significance level, test the claim that it takes the average student less than 5 years to complete a degree. 4, 5, 4.5, 6, 7, 4, 4, 3.5, 4, 9 Find the mean and standard deviation for this sample.

2.
Find the null and alternative hypothesis for the claim.

3.
Find the test statistic.

4.
Find the P-value or critical value.

5.
Make a conclusion about the claim.

Answer 1

Test: Population mean is known but not standard deviation ---> single-sample t test

 Population Mean (µ )=5

No of sample (n)=10

Degree of fredom(df)=n-1=9

Sample Mean(X bar)=(4+5+4.5+6+7+4+4+3.5+4+9)/10=5.1

Sample standard deviation(s)= 1.744

 

Q(2)

H0:µ =5

H1:µ <5  (one tail test)

 

Q(3)

Calculated test value(t)=(5.1-5)/{(1.744/√10)}= 0.181

 

Q(4)

The P-Value is 0.430113. The result is not significant at p < 0.05.

 

Q(5) t_calculated>t_critical so we reject Null Hypothesis and accept alternative Hypothesis

Hence

it is claimed that it takes the average student less than 5 years