An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 41 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level?

Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Part (a)
Part (b)
Part (c)
Part (d)
State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom.)

Incorrect: Your answer is incorrect.
Part (e)
What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)

Correct: Your answer is correct.
=
Incorrect: Your answer is incorrect.
Part (f)
What is the p-value? (Round your answer to four decimal places.)


Explain what the p-value means for this problem.
If
H0
is false, then there is a chance equal to the p-value that the average time needed to complete an undergraduate degree is 5.1 years or more.
If
H0
is true, then there is a chance equal to the p-value that the average time needed to complete an undergraduate degree is 5.1 years or more.
If
H0
is false, then there is a chance equal to the p-value the average time needed to complete an undergraduate degree is not 5.1 years or more.
If
H0
is true, then there is a chance equal to the p-value the average time needed to complete an undergraduate degree is not 5.1 years or more.
Correct: Your answer is correct.
Correct! A p-value is the probability that an outcome of the data will happen purely by chance when
H0
is true.
Part (g)

Part (h)
Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
=

(ii) Decision:
reject the null hypothesis
do not reject the null hypothesis
Correct: Your answer is correct.

(iii) Reason for decision:
Since > p-value, we reject the null hypothesis.
Since > p-value, we do not reject the null hypothesis.
Since < p-value, we reject the null hypothesis.
Since < p-value, we do not reject the null hypothesis.
Correct: Your answer is correct.

(iv) Conclusion:
There is sufficient evidence to conclude that the average time it takes to finish the undergraduate degrees is longer than 4.5 years.
There is not sufficient evidence to conclude that the average time it takes to finish the undergraduate degrees is longer than 4.5 years.
Correct: Your answer is correct.
Part (i)
Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to two decimal places.)
WebAssign Plot