This module provides a practice of Hypothesis Testing of Single Mean and Single Proportion as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.
Student learning outcomes
The student will conduct a hypothesis test of a single mean with known population standard deviation.
Given
Suppose that a recent article stated that the mean time spent in jail by a first–time convicted burglar is 2.5 years. A study was then done to see if the mean time has increased in the new century. A random sample of 26 first–time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was 3 years with a standard deviation of 1.8 years. Suppose that it is somehow known that the population standard deviation is 1.5. Conduct a hypothesis test to determine if the mean length of jail time has increased. The distribution of the population is normal.
Hypothesis testing: single mean
Is this a test of means or proportions?
Means
State the null and alternative hypotheses.
:
:
(or,
)
Is this a right-tailed, left-tailed, or two-tailed test?
How do you know?
right-tailed
What symbol represents the Random Variable for this test?
In words, define the Random Variable for this test.
The mean time spent in jail for 26 first time convicted burglars
Is the population standard deviation known and, if so, what is it?
Yes, 1.5
Calculate the following:
3
1.5
1.8
26
Since both
and
are given, which should be used? In 1 -2 complete sentences, explain why.
State the distribution to use for the hypothesis test.
Sketch a graph of the situation. Label the horizontal axis. Mark the hypothesized mean and the sample mean
. Shade the area corresponding to the p-value.
Find the p-value.
0.0446
At a pre-conceived
, what is your:
Decision:
Reason for the decision:
Conclusion (write out in a complete sentence):
Reject the null hypothesis
Discussion questions
Does it appear that the mean jail time spent for first time convicted burglars has increased? Why or why not?
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits