STAT
Introduction to Statistics – MATO 205
Test 4: Chapters 8 and 10
Name ______________________________________________ Date _______________
Instructions: You are required to work the questions independently. Do not seek help from
anyone. Follow Hampton University Code of Conduct.
Fill in the space. (2 Points Each)
The ________ __________________ is the opposite of the alternative hypothesis, and will always include equality.
We commit a Type II error when we ________ __ _____________ the null hypothesis when it is actually false.
The probability of committing a Type I error is equal to the ______________________.
The _________ ______________________. Based on the sample information, is used to determine whether to reject the null hypothesis.
To conduct a test of proportions, the value of and must be at least________ (1, 5, 30, 1000).
The __________ value separates the region where the null hypothesis is rejected from the region where it is not rejected.
When conducting a test of hypothesis for means (assuming a normal population), we use the standard normal distribution when the population ______________ ______________ is known.
In a __________ -tailed test, the significance level is divided equally between the two tails. (one, two, neither).
As the degrees of freedom increase, the -distribution _____________ . (approaches the binomial distribution, exceeds the normal distribution, approaches the distribution, becomes more positively skewed)
From earlier studies, it is believed that the percentage of students favoring a four-day school week during May and June of every school year is approximately 85%. What is the minimum sample size that will create a margin of error of 2% with 90% confidence?
79
93
146
541
863
Free Response Question
You Must Show All Your Work to Earn Full Credit. (20 points each)
Suppose that you sample 59 high school baseball pitchers in one county and find that they have a mean fastball pitching speed of 80.00 miles per hour (mph) with a standard deviation of 4.98 mph. Find a 95% confidence interval for the mean fastball pitching speed of all high school baseball pitchers in the county. Interpret the interval. Assume that the fastball ball pitching speeds are normally distributed.
The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 1.4 liters. A health campaign promotes the consumption of at least 2.0 liters per day. A sample of 10 adults after the campaign shows the following consumption in liters: 1.5 1.6 1.5 1.4 1.9 1.4 1.3 1.9 1.8 1.7
At the 0.01 significance level, can we conclude that water consumption has increased?
State the null and alternate hypothesis.
How many degrees of freedom are there?
Give the decision rule.
Compute the value of t. What is your decision regarding the null hypothesis?
The board of a major credit card company requires that the mean wait time for customers when they call customer service is at most 3.00 minutes. To make sure that the mean wait is not exceeding the requirement, an assistant manager tracks the wait times of 45 randomly selected calls. The mean wait time was calculated to be 3.40 minutes. Assuming the population standard deviation is 1.45 minutes, is there sufficient evidence to say that the mean wait time for customers is longer than 3.00 minutes with a 95% level of confidence?
State the null and alternate hypothesis.
Determine which distribution to use for the test statistic, and state the level of significance.
Calculate the necessary sample test statistics.
Draw a conclusion and interpret the decision.
The National safety council reported that 52% of American turnpike drivers are men. A sample of 300 cars traveling southbound on the New Jersey Turnpike yesterday revealed that 170 were driven by men. At a 99% level of confidence, can we conclude that a larger proportion of men were driving on the New Jersey Turnpike than the national statistics indicate?
State the null and alternate hypothesis.
Determine which distribution to use for the test statistic, and state the level of significance.
Calculate the necessary sample test statistics
Draw a conclusion and interpret the decision.