In this lab we will be comparing two population means by comparing sample means drawn independently from different populations.  We will do this by performing tests of significance.
 

1. Are females hotter than males?  Believe it or not, we can answer this question with statistics.  A data set containing the body temperatures and heart rate for 65 men and 65 women can be found here.  We will use this data set to answer the questions:  "Do women have a higher mean body temperature than men?" and "Do women have a higher heart rate than men?"

1. Find the mean body temperatures and mean heart rates for both men and women. (Stat > Basic Statistics > Display Descriptive Statistics.  Make sure you click on By variable: and put Gender in the box.)  Which group has the higher sample mean temperature? Which group has the higher sample mean heart rate?
2. Make side-by-side boxplots for the body temperatures for both genders.   (Graph > Boxplot > One Y with Groups).  Put  Temp in for the Graph variables: and Gender in for the Categorical variables:).  Make sure the pair of boxplots is labeled appropriately.
3. Make side-by-side boxplots for the heart rates for both genders.
4. Complete a two-sample t test to see if the mean body temperature for females, in general, is higher than the mean body temperature for males. (Stat > Basic Statistics > 2-Sample t.) Make sure you choose the appropriate alternative hypothesis.  Report the hypotheses, P-value, and conclusion.
5. Complete a two-sample t test to see if the mean heart rate for females, in general, is higher than the mean heart rate for males. (Stat > Basic Statistics > 2-Sample t.) Make sure you choose the appropriate alternative hypothesis.  Report the hypotheses, P-value, and conclusion.

 
2. The Berkeley Guidance Study was a longitudinal study that monitored the height and weight of boys and girls born in Berkeley, California between January 1928 and June 1929.  A sample of this data set was obtained from Applied Linear Regression, 2nd Edition, by Sanford Weisberg.  This data set includes the heights, in centimeters, for boys and girls at ages 2, 9, and 18.  These heights can be found here.

1. You need to make 3 sets of side-by-side boxplots here.  One set for the boys and girls at age 2, one set for boys and girls at age 9, and one set for boys and girls at age 18.  Make sure each pair of boxplots is labeled appropriately.
2. Based on your three pairs of boxplots, do you think the mean height of the boys is statistically significantly higher than that of the girls at age 2, 9, or 18?
3. Complete three two-sample t tests to see if the mean height of the boys is higher than that of the girls at age 2, 9, or 18?  Make sure you choose the appropriate alternative hypotheses.  Report the hypotheses, P-value, and conclusion.