Question

4) Last year we went to Zanvoort Circuit Park in North Holland to retest how many laps women and men drivers could do in half an hour. Historical data available gave us a basis for standard deviations of 3.5 and 2.63 laps, respectively Use men pilots as  x̄1. Below are the summaries of our new findings:

(Show all work for credit. Including Normalcdef(a,b,c,d), INVorm(a,b,c) z, z*,SD,SE and CI.Do not forget to check conditions for each story, and sketches for hypothesis only. Round answers to the nearest five decimal places. PLEASE BE NEAT (If you can handwrite the answer to this question PLEASE), and show all formulas!!!)

Laps/30 minutes	Mean	SD	n
Women pilots	17.91	3.39	50
Men pilots	19.39	2.52	50

a) Find a 95% confidence interval for the difference here. Explain the meaning of the results.

b) Now perform the appropriate hypothesis test, and explain your results.

Answer 1

Answer:-

Given That:-

4) Last year we went to Zanvoort Circuit Park in North Holland to retest how many laps women and men drivers could do in half an hour. Historical data available gave us a basis for standard deviations of 3.5 and 2.63 laps, respectively Use men pilots as  x̄1.

a) Find a 95% confidence interval for the difference here. Explain the meaning of the results.

Level of Significance , α = 0.05
z-critical value = Z α/2 = 1.960 [excel function =normsinv(α/2) ]
  
std error , SE = √(σ1²/n1+σ2²/n2) = 0.5974
margin of error, E = Z*SE = 1.960 * 0.597 = 1.170822
  
difference of means = x̅1 - x̅2 = 17.91 - 19.39 = -1.480
confidence interval is   
Interval Lower Limit= (x̅1 - x̅2) - E = -1.480 - 1.171 = -2.6508
Interval Upper Limit= (x̅1 - x̅2) + E = -1.480 + 1.171 = -0.3092

b) Now perform the appropriate hypothesis test, and explain your results.

Ho : µ1 - µ2 = 0
Ha : µ1-µ2 < 0
  
Level of Significance , α = 0.05
  
sample #1 ------->
mean of sample 1, x̅1= 17.9100
population std dev of sample 1, σ1 = 3.39
size of sample 1, n1= 50
  
sample #2 --------->
mean of sample 2, x̅2= 19.3900
population std dev of sample 2, σ2 = 2.52
size of sample 2, n2= 50
  
difference in sample means = x̅1 - x̅2 = 17.91 - 19.39 = -1.48
  
std error , SE = √(σ1²/n1+σ2²/n2) = 0.5974
  
Z-statistic = ((x̅1 - x̅2)-µd)/SE = -1.48 / 0.5974 = -2.478
  
Z-critical value , Z* = -1.6449 [excel function =NORMSINV(α)]
  
p-value = 0.0066 [excel function =NORMSDIST(z)]
Desison: p-value <α , Reject null hypothesis
  
Conclusion: There is enough evidence to conclude that men drivers could do more laps in half an hour

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