In this lab we will be comparing two population means by comparing sample means drawn independently from different populations.  We will also compare two population proportions.
 

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.

3. A study of the comparison of the proportion of boys born to smoking parents to that of  nonsmoking parents was reported on April 20, 2002 by The Lancet, a British medical journal.  The results of the article showed that couples who smoke around the time of conception are less likely to produce boys than those that do not.

1. One of the statistics reported was that out of 565 births where both parents smoked more than a pack a day, 255 were boys.  What proportion of these births resulted in a boy?  Based on this proportion, find a 95% confidence interval for the proportion of all births, where both parents smoke, that would result in a boy.  (Stat > Basic Statistics > 1 Proportion  click on Summerized data: and put in the appropriate numbers.  It should default to use a 95% confidence interval.)
2. Another statistic reported was that out of 3602 births where both parents did not smoke, 1975 were boys.  What proportion of these births resulted in a boy?  Based on this proportion, find a 95% confidence interval for the proportion of all births, where neither parent smoke, that would result in a boy. 
3. Is the proportion of boys born to parents that do not smoke higher than the proportio of boys born to parents that smoke?  Test this at the 5% signficance level.  Make sure you report your hypotheses, P-value, and conclusion.  (Stat > Basic Statistics > 2 Proportions then click on Summarized data: and put the results for the nonsmoking parents in for the First sample: and the smoking parents in for the Second sample:.  Under Options..., click on greater than for the alternative hypothesisl.)