Question

The average income in France is £56,516. A team of researchers is interested to see the impact of geographical location on income. A sample of 35 participants from the northeastern region of France were asked to provide their income. The average income was £49,520 with a standard deviation of £1,200.

1. Which test will you use to determine significance? One tail or two tail?

2. State the null and alternative hypotheses

3. State your research criteria

4. Calculate your test statistic

5. State your decision regarding significance

6. Calculate the confidence interval, if applicable.

7. Calculate the effect size and proportion of variance, if applicable.

Answer 1

(1) Two tail

(2) Ho: μ = 56516 and Ha: μ ≠ 56516

(3) We will use a one sample t test to see if the northeastern France has income different from the national average. We will use α = 0.05. We will reject Ho if the test p- value < 0.05.

(4 and 5)

Data:     

n = 35    

μ = 56516    

s = 1200    

x-bar = 49520    

Hypotheses:    

Ho: μ = 56516    

Ha: μ ≠ 56516    

Decision Rule:    

α = 0.05    

Degrees of freedom = 35 - 1 = 34

Lower Critical t- score = -2.032244498   

Upper Critical t- score = 2.032244498   

Reject Ho if |t| > 2.032244498   

Test Statistic:    

SE = s/√n = 1200/√35 = 202.8370211   

t = (x-bar - μ)/SE = (49520 - 56516)/202.837021134844 = -34.4907

p- value = 0   

Decision (in terms of the hypotheses):   

Since 34.49074514 > 2.032244 we reject Ho and accept Ha

Conclusion (in terms of the problem):   

There is sufficient evidence that the northeastern France has income significantly different from the national average

(5)

n = 35     

x-bar = 49520     

s = 1200     

% = 95     

Standard Error, SE = s/√n =    1200/√35 = 202.8370211

Degrees of freedom = n - 1 =   35 -1 = 34   

t- score = 2.032244498     

Width of the confidence interval = t * SE =     2.03224449783959 * 202.837021134844 = 412.2144202

Lower Limit of the confidence interval = x-bar - width =      49520 - 412.21442015946 = 49107.78558

Upper Limit of the confidence interval = x-bar + width =      49520 + 412.21442015946 = 49932.21442

The 95% confidence interval is [$49408, 49932]

(6) Effect size = |49520 - 56516|/1200 = 5.83