Null Mother who smoke have the averagelevel of education as those who do not smoke. Alternative: mothers who smoke do not have the same level of education as those who do not smoke.
Problem 2.
If there were no difference in average education level for the two groups, we would expect to see a difference as large or larger than the one that we saw in about 1% of all samplesof this size.
Problem 3.
a) Null Calcium does not have an impact on the severity of premenstrual symptoms. Alernative: Calcium does reduce the severity of premenstrual symptoms.
b) Type 1, concluding calcium has an impact when it does not.
c) The consequence of a type 1 error is that some women may ake calcium because they have been told that it would reduce premenstrual symptoms, but in fact it does not. The consequence of a type 2 error is that women are told that calcium is not effective, and thus do not take it, when in fact it would help reduce symptoms.
Problem 4.
a) Null: the calcium and placebo treated participantscame rom populations with equally sever PMS mood swings. Alternative: the calcium and placebo treated participants came from populations with PMS mood swings of different severity. Conclusion|: the null hypothesis is not rejected; the two sets of participants do not come from different populations.
Problem 5.
a) Null: Psychotherapy and desipramine are equally effective is treating cocaine use. Alternative: one method is more effective than the other.
b) A type 1 error would occur if there is no difference in the treatments, but the conclusion is that they do differ. A type 2 error would occur if there is a more effective treatment but the study fails to make that conclusion.
c) Type 1; concluding that there is a difference when there isn't.
Problem 8.
We do not specify a particular value fo the population when we state the alternative hypothesis, so there is no way to determine what to expect by chance as there is when we assume that the null hypothesis is true.
Problem 11.
a) There is no statistically significant difference
b) Conclude that there is a statistically significant difference.
Problem 14.
a) 2.0
b) about the 97.75th percentile
c) The corresponding p-value is about 0.025, which is less that 0.05, so the null hypothesis is rejected.
d) The alternaive hypothesis contains a whole range of values, from just above 0.25 to 1. Therefore we would not know what to use as the mean and standard deviation.
Problem 15.
a) No! there will be one or two false positives per 100 infected people tested, and because there is no way to know who they are they would not be retested. Their contaminated blood wouldend up in the blood supply.
b) of the 100 infected, 99 would test positive. of the 9,900 notinfected, 1% or 99 would test positive, so the probability of actually being infected given a positive test is 0.5.
Problem 17.
THey should use a higher p-value, thus increasing th probability of making a type 1 error and reducing the probability of a type 2 error.
Problem 18.
Type 1 error would be that there is no relationship between aspirin and heart attack, but that the study found one. People would start taking aspirin needlessly, Type 2 error is that aspirin does help prevent heart attacks but that the study not discover the relationship, so that people who could have been helped by taking aspirin are not told to take it.