BIOL 300 – Assignment #3: Testing Hypotheses and Confidence Intervals

(Due: Mar. 16th)

1.  A sample of 41 largemouth bass was taken from a lake in order to test whether the size of the fish is greater than a standard of 250 mm. The measures approximately followed a normal distribution, with a sample mean of 272.8 and a sample standard deviation of 96.4.

(a)  Are these fish significantly above the standard, using a significance level of 0.05?

(b)  If our conclusion from part (a) was incorrect, then what type of error have we made?

(c)  Create a 99% confidence interval for the mean length of these fish.

2.  Clean Air standards require that vehicle emissions are tested every 2 years, and if they are too high, the car will require repairs before one can drive it. Suppose that the province regulators double check a random selection of cars that a not-so-trustable shop has certified as ok. They will revoke the shop’s license if they find significant evidence that the shop is certifying vehicles that do not meet standards.

(a)  In the context of this example, what is a Type I and Type II error?

(b)  If you are the shop owner, which would you consider more serious?

(c)  If you are an environmentalist, which would you consider more serious?

3.  National data in the 1960’s showed that about 44% of the adult population had never smoked cigarettes. In 1995, a national health survey interviewed a random sample of 881 adults and found that 52% had never been smokers.

(a)  Create a 90% confidence interval for the proportion of adult (in 1995) who had never been smokers.

(b)  If we want the above confidence interval to have a margin of error no larger than 1%, then how large a sample should we take?

(c)  Test if the proportion of never-smokers in 1995 is significantly greater than 44%, using a significance level of 5%

4. For your honours project in biology, you have decided to test the effects of studying on nervous tics in students. You collect data on 100 of your Biology 300 classmates, picked at random. You split these students into two groups of 50; one group, the "study" group, stays up all night studying for the Biology 300 Midterm. The other group, the "party" group, pursues alternative activities. On the morning of the exam, you measure the rate at which each group of student displays nervous tics, such as coughing, flinching, and sudden blinking of the eyes. You come up with the following data, and you may assume that the data come from a normal distribution.

Group / Sample Size / Mean / SD
Study / 50 / 123.5 / 10.2
Party / 50 / 117.9 / 9.4

(a)  Test if the mean tick rate is the differrent for the party and study group, using an alpha of 1%. You may assume that the variances are equal.

(b)  Create a 99% confidence interval for the difference of mean tick rates.

(c)  State how you can use the confidence interval you made in part (b) to answer part (a).

(d)  What is the probability that we make a Type I error?