Note Your answers to the questions below should follow the expectations for homework found here. Due date is on the Dates page.

## Male-Female Birth Ratio

Davis et al. (1998) observed a decline in the ratio of male to female births in several industrialized countries and explored whether that result was an indicator of larger health issues. The data below are the proportion of male births (PropMale) for the United States. Use these data to answer the questions further below. [Note: The data are wrapped onto multiple lines simply to save space. Carefully check that your data entry is correct.]

```Year:       1970   1971   1972   1973   1974   1975   1976
PropMale: 0.5134 0.5126 0.5125 0.5128 0.5133 0.5132 0.5128

Year:       1977   1978   1979   1980   1981   1982   1983
PropMale: 0.5128 0.5129 0.5127 0.5129 0.5126 0.5123 0.5127

Year:       1984   1985   1986   1987   1988   1989   1990
PropMale: 0.5122 0.5126 0.5122 0.5120 0.5121 0.5120 0.5120
```
1. Is there evidence for a significant statistical change in the proportion of male births in the U.S. over the study period?
2. At what average annual rate (i.e., how much per year) did the proportion of male births change? [Be specific about the direction of change.]
3. Explain why the p-value for the slope is so small even though the value of the estimated slope is such a small number [i.e., how is it possible that such a small value for the slope can be considered to be different from zero?].

## Ashland Climate

Climate scientists often need to understand the relationship between different climate variables and particular locations. One area of interest for specific models is an estimate of the relationship (if any) between average monthly preciptation and average monthly temperature (such that preciptation may be predicted from temperature). Average monthly high and low temperatures and preciptation for Ashland, WI can be found on this Wikipedia page). Load the average high (be careful, NOT the record high) and average preciptation from this page into R and use it to answer the questions below. [Note: Please use metric units for both variables]

1. Is there a significant relationship between average monthly precipitation and average monthly high temperature for Ashland, WI? If so, specifically describe that relationship (with appropriate interval)?
2. Interpret the value of the intercept (with appropriate interval) from your regression model and comment on whether is is proper to interpret this value.
3. Predict (with appropriate interval) the mean average monthly precipitation if the average monthly high temperature is 10oC.
4. Predict (with appropriate interval) the average monthly precipitation if the average monthly high temperature is 10oC.