Hypothesis Testing, Example 1:
Bicyclists race on set route. The time of a cyclist drawn at random is randomly distributed with an
approximately normal distribution with mean of 87 minutes and a standard deviation of 6 minutes.
A bicycling coach claims to have a new training technique which will reduce times.
We will test this claim by sampling 10 bicyclists who use this technique and measure their time on
the same route.
State the null hypothesis:
State the alternative hypothesis:
Is this a one tail or two tail test? If one tail, which?
Since the standard deviation is given, we will use which statistic?
We will use an alpha of 5%. What does this mean?
What is the value of the critical value?
Draw a bell curve to show the above.
The sample of the 10 cyclists has a sample mean of 85 minutes.
What is the resulting test statistic?
What is the conclusion of the hypothesis test?
What is the p-value? What does that mean?
Hypothesis Test 2
Quality Control. Pyrex makes measuring cups. A “one cup” measuring cup must be able to
measure a cup of liquid to within 2% of an actual cup. That is, a manufactured measuring cup
should measure 8 ounces plus or minus 2% (=+/- .16 ounces). Assume any errors from one cup are
distributed normally. A manufactured cup’s measurement has a mean of 8 ounces and a standard
deviation of .12 ounces.
QC person will test 5 measuring cups and test their accuracy.
State the null hypothesis:
State the alternative hypothesis:
Is this a one tail or two tail test? If one tail, which?
Since the standard deviation is given, we will use which statistic?
We will use an alpha of 10%. What does this mean?
What is the value of the critical value?
Draw a bell curve to show the above.
The sample of the 5 cups has a sample mean of 8.08 ounces.
What is the resulting test statistic?
What is the conclusion of the hypothesis test?
What is the p-value? What does that mean?
Hypothesis Test 3
Cabrillo College is curious about how far the average person drives to the college. They wonder if
the average person drives less than 10 miles. We’re going to randomly sample 35 students to see.
State the null hypothesis:
State the alternative hypothesis:
Is this a one tail or two tail test? If one tail, which?
Since the standard deviation is NOT given, we will use which statistic?
We will use an alpha of 1%. What does this mean?
What is the value of the critical value?
The sample shows a mean of 9.8 miles and a standard deviation of 5.4 miles.
What is the resulting test statistic?
What is the conclusion of the hypothesis test?
What is the p-value? What does that mean?
What would be an easy way to make this problem slightly more complicated?