USE EXCEL AND SHOW FORMULAS USED IN EXCEL TO COMPLETE THE PROBLEM You are compar

Question

USE EXCEL AND SHOW FORMULAS USED IN EXCEL TO COMPLETE THE PROBLEM

You are comparing the volume of traffic through two intersections on alternate routes. The Problem data file provides data for the number of cars per hour for each intersection over a 24 hour period.

A. Prove, to 95% confidence, that intersection A has more traffic (per hour) than intersection B.

B. What is the observed significance level for the result?

1 7 4 9 4 10 8 11 9 15 141 125 125 122 90 99 84 86 76 77 59 77 45 40 46 41 53 44 54 54 56 61 249 148 165 129 18 18 21 22 21 29 26 30 26 35 28 40

Explanation / Answer

As the data is paired here for each hour of a day so we will use t - test for paired data

Null Hypothesis: H0 : Traffic at Intersection A = Traffic at Intersection B. A-B = 0

Alternative Hypothesis: Ha : Traffic at Intersection A > Traffic at Intersection B. A-B > 0

Now here confidence level is 95% so alpha would be 0.05 and in one direction only.

Test statistic

We will use excel function Data -> Data Analysis -> t: test: Paired two sample for means.

and put mean difference = 0 and alpha = 0.05 and get this result

it can be calculated by this difference table

so Test statistic

t = (A-B -0)/ (sd /sqrt(n)) = 3.33/ (23.32/sqrt(24)) = 3.33/ 4,76 = 0.700

Part b.. is the observed significane level or p- value = 0.2454 as calculated above

t-Test: Paired Two Sample for Means Route 1 Route 2 Mean 58.7083333 55.375 Variance 3606.38949 1839.983696 Observations 24 24 Pearson Correlation 0.9515757 Hypothesized Mean Difference 0 df 23 t Stat 0.70021466 P(T<=t) one-tail 0.24540807 t Critical one-tail 1.71387152 P(T<=t) two-tail 0.49081615 t Critical two-tail 2.0686576

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