Question

A set of numbers such as those below is meaningless without some background information. The INDIVIDUALS here are Newcomb's 66 repetitions of his experiment. We need to know exactly WHAT VARIABLE he measured, and in WHAT UNITS. Newcomb measured the time in seconds that a light signal took to pass from his laboratory on the Potomac River to mirror at the base the Washington Monument an back, a total distance of about 7400 meters. Just as you can compute the speed of a car from the time required to drive a mile, Newcomb could compute the speed of light from the passage of time. Newcomb's first measurement of the passage of time of light was 0.000024828 second or 24828 nanoseconds. The entries above record only the deviation from 24800, so the first entry, 28, is short for 24828 nanoseconds. Negative entries are numbers less than 24800.

28	22	36	26	28	28
26	24	32	30	27	24
33	21	36	32	31	25
24	25	28	36	27	32
34	30	25	26	26	25
-44	23	21	30	33	29
27	29	28	22	26	27
16	31	29	36	32	28
40	19	37	23	32	29
-2	24	25	27	24	16
29	20	28	27	39	23

Use the data set above to make a histogram and analyze it, using key terms

Present a 5 number summary and a modified box plot and are there any outliers?

Report the mean and standard deviation (do not discard outliers), the mean was important in this experiment. Calculate the 95% confidence interval for the true mean. Explain what this means.

Compare these (5 number summary and mean/standard deviation). Are the mean and standard deviation valid for this set of data? Justify your answer.

Some of the above (and what follows below) makes no sense if the data is not approximately normal. Explain what this means. Is this data close to normal distributed? Justify your answer. Regardless of your conclusion, for the next part assume the data is approximately normal.

The data listed in the order it was recorded (down first, then across). Do a time plot. Analyze this plot, paying close attention to new information gained beyond what we did above.

Cut the data in half (first three columns vs. last three columns) and do a back to back stem plot. Analyze this. Does this further amplify what the time plot showed?

Calculate the mean of the second half of the data.

Using the mean and standard deviation of the whole data set (found above) as the population mean and standard deviation, test the significance that the mean of the second half is different than the mean of the total using α=.05 . Make sure to clearly identify the null and alternative hypothesis. Explain what this test is attempting to show. Report the p-value for the test and explain what that means. Accept or reject the null hypothesis, and justify your answer (based on the p-value).

Answer 1

Use the data set above to make a histogram and analyze it, using key terms.

Histogram of x 髦3 電y 24760 24780 24800 24820 24840

Present a 5 number summary and a modified box plot and are there any outliers?

24760 24780 24800 24820 24840

> summary(x)
Min. 1st Qu. Median Mean 3rd Qu. Max.
24756 24824 24827 24826 24831 24840

Outliers are 24756, 24798

Report the mean and standard deviation (do not discard outliers), the mean was important in this experiment.

Mean = 24826

standard deviation=  10.74532

Calculate the 95% confidence interval for the true mean. Explain what this means.

95% confidence interval is

$\\24826 \pm 1.96*10.74532\\=(24804.94,24847.060)$

95% of the times our mean will fall in this region.