1. The Census Bureau is planning to take a sample amounting to 1/10 of 1% of the population in each state in order to estimate the percentage of the population in that state earning over $50,000 a year. Other things being equal, which of the following is true (circle one):
(i) The accuracy to be expected in California (population thirty million) is about the same as the accuracy to be expected in Nevada (population one million).
(ii) The accuracy to be expected in California is quite a bit higher than in Nevada.
(iii) The accuracy to be expected in California is quite a bit lower than in Nevada.
Please explain your reasoning.
2. Extensive research conducted during the 1970s demonstrated that pregnancy durations are normally distributed with a mean of 266 days and a standard deviation of 16 days. In a very recent study of 16 pregnancy durations selected at random, the average pregnancy duration was 286 days with standard deviation of 20 days. Does this new study provide evidence that pregnancy durations have increased since the 1970s?
State the null hypothesis and the alternative hypothesis.
Perform a test of significance and state the resulting p-value. What would you conclude?