Answering the following questions.

1. Describing the Data.

a. Provide descriptive statistics for the weight gain observed in this sample.

b. Provide descriptive statistics (n, mean, standard deviation, median, first and third

quartiles, and minimum and maximum) for the weight gain observed in the sample of

women who drank only bottled water versus those who drank only tap water.

c. Use a box-and-whisker plot to compare the distribution of the weight gain of the three

water consumption groups (tap-only, bottle-only, and tap-and-bottle). What does the

plot show?

2. One-Sample Study (tap-only)

a. Estimate (using a 95% confidence interval) the true mean weight gain. Interpret.

b. Abrams et al. (2000) reported that the healthy pregnant women are generally

advised to limit weight gain to approximately 26 pounds. Is the weight gain different

in the sample of women who drank only tap water? Use statistical inference to justify

your answer.

c. Suppose that a normal distribution could not be assumed for the weight change. Use

a signed rank test to determine whether the change in this population is different

from the historical control (26 pounds). Provide an interpretation of the results.

3. Two-Sample Study (tap-only and bottle-only)

a. Provide the null and research hypotheses (defining all symbols) for comparing the

mean weight gain in the two water groups.

b. Use a statistical test to determine whether the variances of the two groups (tap-only

and bottle-only) are different.

c. Based on the response to part (b), perform the appropriate two-sample t-test (equal

or unequal variances). Interpret the results.

d. Based on the response to part (b), provide an interval estimate for the mean

difference in weight gain between the two groups. Interpret.

References

The lab report attached.

2a,b 2a,b The TTEST Procedure The TTEST Procedure Variable: wtgain Variable: wtgain N Mean Std Dev Std Err Minimum Maximum Q-Q Plot of wtgain 270 40.0107 5.7299 0.3487 24.5000 63.9000 O O 60 95% Mean 95% CL Mean Std Dev CL Std Dev 40.0107 39.3242 40.6973 5.7299 5.2840 6.2588 50 - DF t Value Pr > It| 269 40.18 <.0001 wtgain distribution of with confidence interval for mean normal kernel o percent w quantile oo oc wtgainthe univariate procedure variable: moments n sum weights observations std deviation variance skewness kurtosis uncorrected ss corrected coeff variation error basic statistical measures location variability median mode range interquartile tests location: mu0="0" test statistic p value student t pr> It| <.0001 sign m pr>= [MI <.0001 signed rank s pr>= ISI <.0001 quantiles level quantile max q3 median q1 min the univariate procedure variable: wtgain extreme observations lowest highest value obs group="1" moments n sum weights mean std deviation variance skewness kurtosis uncorrected ss corrected coeff variation error basic statistical measures location variability mode range interquartile tests for location: mu0="0" test statistic p student t pr> Itl <.0001 sign m pr>= [MI <.0001 signed rank s pr>= ISI <.0001 quantiles level quantile max q3 median q1 min the univariate procedure variable: wtgain group="1" extreme observations moments lowest highest n sum weights value obs mean std deviation variance skewness kurtosis uncorrected ss corrected coeff variation error basic statistical measures location variability mode range interquartile tests for location: mu0="0" tes statistic p student t pr> It <.0001 sign m pr>= |M| <.0001 signed rank s pr>= |S| <.0001 quantiles leve quantile max q3 median q1 min the univariate procedure variable: wtgain group="2" extreme observations lowest highest value obs distribution of by hih n w2c wtgair moments sum weights lowes mean std deviation variance skewness kurtosis uncorrected ss corrected coeff variation error basic statistical measures location variability mode interquartile range tests for location: mu0="26" test statistic p student t pr> It| <.0001 sign pr>= [M| <.0001 signed rank s pr>= |S| <.0001 quantiles leve quantile max q3 median q1 min the ttest procedure variable: wtgain group method n mean std dev err minimum maximum distribution of diff pooled percent satterthwaite cl variances t value pr> It| O Pooled Equal 583 -5.11 <.0001 o oo of group satterthwaite unequal .4.99 n equality variances wtgain method num df den f value pr> F Normal - Kernel Folded F 269 314 1.90 <.0001 q-q plots of wtgain quantile>