ASSIGNMENT 1
Name_______________
Consider data sets 3 and 4, the last two experiments done by Newcomb, in the handout on Box
& Whisker plots. Use these data sets and the computer printout distributed In class to answer the following questions.Report your answers on this assignment sheet.
1.
Construct a stem and leaf display for data set 4. Order the leaves.
6
6
7
7
8
8
2. Compute the following sample statistics for flat set the values given In the handout may be incorrect.
Maximum = ___________ Minimum = ___________
Upper quartile = ___________ Lower quartile = ___________
Median = ___________ Mean = ___________
Variance = ___________ Std. deviation = ___________
Skewness = ___________ Kurtosis = ___________ ．
3. Assuming that the observations in data set 4 are NID( μ , σ 2
), construct a 95% confidence interval for the population mean. lower limit = _____________ upper limit = _____________
Also construct a 90% confidence interval for the population variance lower limit = _____________ upper limit = _____________
4. Using the assumptions made in problem 3, test the null hypothesis that the population mean is
765 against the two-sided alternative that it is not 765. Report values for the t-statistic = ___________ d.f. = ___________
_____________ ≦ p-Value ≦ _____________

5.An Important question is whether the same quantity was measured with the same precision in the last two experiments done by Newcomb. Examine the computer output distributed in class.
Compare the stem and leaf displays and the box plots for the two displays. Do the observations appear to have been sampled from the same population of possible values?
Yes No (circle one)
6. Comparing graphs and other forms of data displays is a subjective endeavor and there can be disagreements among decision makers, especially those with little experience in looking at such displays. One solution is to develop more precise mathematical measures for the differences in data sets. The procedures we will use are based on normal, or Gaussian, probability models for the underlying populations. Before applying those procedures it makes sense to check if the model assumptions are at least approximately satisfied. Examine the normal probability plots, or rankit plots, for data sets 3 and U from the SAS output. Report the values for the
Shapiro-Wilk statistics.
Is there sufficient evidence to conclude that ether population of possible values is not normal? possible
Data set 3 : n = ___________ W = ___________ p-value = ___________
Data set 4 : n = ___________ W = ___________ p-value = ___________
Yes No (circle one)
7.Consider the graphs of the observations against the order in which they were taken. Does the variation in the observations appear to be constant with respect to order for each data set?
Yes No (circle one)
Does either data set exhibit the kind of aerial correlation, or lack of independence, observed in data set 5, which was examined in class?
Yes No (circle one)
Perform the test for ”too few runs” for data sets 3 and 4. Report the following:
Data set 3 : n1 = ___________ u = ___________ p-value = ___________
Data set 4 : n1 = ___________ u = ___________ p-value = ___________

8. Regardless of your conclusions in parts 6 and 7, assume that each data set was obtained by random sampling from a normal population. Test the null hypothesis that the population variances are the same. Use an F-test. Report the values for the
F-statistic = ___________ d.f. = ___________
_____________ ≦ p-Value ≦ _____________
State your conclusion.
9. Regardless of your conclusions in parts 6, 7, and 8, assume that the observations in data set 3 are
NID( μ
1
, σ 2
) and the observations in data set 4 are NID( μ
1
, σ 2
). Also assume the observations in data set 3 are independent of the observations in data set 4. Construct a 90% confidence interval for difference of the population means. lower limit = _____________ upper limit = ____________
10.Test the null hypothesis that the two population means are equal in part 9 against the two-sided alternative that the population means are not equal. Report the values for t-statistic = __________ d.f. = ___________
_____________ ≦ p-Value ≦ _____________
State your conclusion. Comment on whether you believe that Newcomb was measuring the same quantity in the two experiments. If there is evidence from parts 6,7, and 8 that the model assumptions used in parts 9 and 10 are violated, discuss how the inferences reached in parts 9 and
10 are affected by the violations of the model assumption.