Snow totals at different elevations

The table below contains observations of the top 10 snowfalls (in feet) at two locations (high and low elevations).

Event # High Elevation station A Low elevation Station B

1 55.60 21.50

2 47.65 21.35

3 33.50 19.35

4 28.75 17.85

5 21.95 16.35

6 18.50 10.50

7 17.65 7.95

8 16.80 7.15

9 15.25 4.75

10 13.75 3.45

The sample means and SDs are as follows:

Higher elevation station A: Mean of 26.94, SD of 14.50

Low Elevation station B: Mean 13.02, SD of 7.01

1] Perform a two-sample t test on this data set to evaluate whether or not snow totals are statistically greater at the higher elevation station.

2] Is this a one-tailed OR two-tailed test? Explain.

3] State your nul and research/alternate hypotheses.

4] Test these at BOTH the 5% and 1% significance level. What are your t-critical values at the 5% and 1% levels?

5] State your conclusion at the 5% level. Include statements about whether you rejected or failed to reject your Null hypothesis etc. Is there a statistica y significant increase in snowfall at the higher elevation station at the 5% level?

6] State your conclusion at the 1% level. Include statements about whether you rejected or failed to reject your Null hypothesis etc. Is there a statistically significant increase in snowfall at the higher elevation station at the 1% level?

7] Go back to the table in the book where you found your critical values. What number of "degrees of freedom" would have caused you to draw different conclusions at both the 5% and 1% significance levels? What does this tell you about the relationship between sample size and rejecting the null hypothesis? Does having a larger sample make it easier or more difficult to exceed a critical t-value? Explain. ** NOTE: Statistically-speaking, the confidence level is the probability that your sample statistic falls in the body of the curve, whereas the significance level is the probability it does not fall in the body of the curve.

8a] Using the above definitions, in which test [#5 at the 5% level OR #6 at the 1% level] would you have more statistical confidence? Why? (Hint--the answer has nothing to do with the actual numbers you calculated--it is purely a question about the relationship between statistical significance and confidence).

8b] If the significance level was 0.01, what would be your confidence level? (Recall that the two together equal the total area under the normal curve.)