Math 2210---Hypothesis testing examples I.
0. (a fake problem) Suppose that in Fall 2013, the number of credit hours attempted by AU students was
normally distributed with mean 12.5. Because students are being encouraged to take full loads, it is believed
that this number should increase in the future. In Fall 2014, the mean number of credits attempted by the
1800 new freshmen was normally distributed with mean 12.9 and standard deviation 3.1. Determine if this
represents a statistically significant increase in the mean number of hours attempted, using 𝛼 = .01to make
your conclusion. Under what conditions would you conclude there has been a significant increase in the
mean number of hours attempted?
1. It is believed that the 7:30 nightly flight between Atlanta and Augusta departs an average of 22 minutes
behind schedule. Further, the departure delays are normally distributed. Now, congestion at the Atlanta
airport is getting progressively worse, and the airline wonders if the delays are also getting worse, so they
obtain a sample of 15 ATL-AGS flights and found the number of minutes those flights departed behind
schedule was as follows:
39
31
18
7
48
28
48
22
24
27
38
18
23
28
37
On the basis of this data, determine if this represents a significant increase in the average departure delay for
this particular flight. Use 𝛼 = .01 to make your conclusion, and assume that an increase in delays is the
airline’s only concern.
2. See problem 1. What if you used 𝛼 = .05? In general, what happens if a higher/lower significance level is
used?
3. Healthy humans typically have a blood Ph of about 7.4 and the Ph levels are normally distributed. To test
a new drug, a sample of 11 physiologically similar patients (with mean blood Ph 7.4) is obtained. One of its
possible side effects is that the drug may alter the patient's blood Ph. The blood Ph of these 11 patients is
measured after they begin taking the drug, and the data is below.
8.7
7.8
7.5
7.6
7.4
7.4
8.0
7.3
9.3
8.2
8.2
Test the hypothesis that the drug does in fact alter Ph levels. Use 𝛼 = .10.
4. Historically, the grades in a certain college course have been normally distributed with mean grade (A=4,
B=3, …) 2.20. A new professor is teaching a large section of that class with 70 students, and their grade
distribution is:
9 A, 17 B, 24 C, 10 D, 10 F.
Determine if the grades in that section of the course were unusually low, using 𝛼 = .05.
5. An auto manufacturer claims that a certain model car should average 28 mpg in city driving. A consumer
group wants to test if this claim is accurate, so they test drive the car, using 10 tanks of fuel in typical city
conditions. The observed fuel economies in these 10 tanks were:
27.4
28.8
28.2
25.6
26.2
26.2
27.4
29.8
26.3
28.6
On the basis of this data, determine if it should be concluded that this model car averages less than 28 mpg in
city driving. Use 𝛼 = .01 to make your conclusions, and assume the fuel economy in a given tank is normally
distributed. Note: presumably the only alternate of interest is if the mileage is less than advertised.
6. See problem 5. Suppose I then were to tell you that I generated that sample data from a normally
distributed population whose mean was 27.4 (which is how that data was generated, by the way). What
happened in problem 5?
7. Clayton Kershaw is probably the best pitcher currently in the major leagues, largely because he strikes out
lots of hitters while having excellent control. In his first 6 years in the league, Kershaw walked only 8.3% of
the batters he faced. In 2014, Kershaw walked 31 of the 749 batters he faced. Determine if Kershaw’s walk
rate in 2014 was significantly lower than it had been in the 6 seasons prior.
8. In a series of recent New Jersey polls*, 2752 likely voters were polled, and 50.8% of them indicated that
they were inclined to vote for Hillary Clinton in the upcoming presidential election. At a similar stage of the
2012 election, Barack Obama was polling at 52.3% in New Jersey. Determine if in fact Clinton’s New Jersey
poll numbers show a significant difference from Obama’s New Jersey poll numbers at this point in the
campaign season. Use a 5% significance level to make conclusions.
*-one of the few states where I could find a direct Hillary-or-Trump poll without any of the third-party
candidates in the mix (which complicates the analysis!)