4. Listed below are the numbers of years that popes and British monarchs (since

Question

4. Listed below are the numbers of years that popes and British monarchs (since 1690) lived after their election or coronation. Treat the values as a simple random samples from a large population. Use 0.01 significance level to test the claim that the mean longevity for popes is different from the mean for British monarchs after coronation Popes: 2 9 21 3 6 10 18 11 6 25 23 6 2 15 32 25 11 8 17 19 5 15 0 26 Kings and Queens: 17 6 13 12 13 33 59 10 7 63 9 25 36 15 ) est the clsim using a bypothesis test (b) Test the claim by constructing an appropriate confidence interval. Confidence Interval: Conclusion: (c) Based on the results, is there sufficient evidence to support the claim that the mean longevity for popes is different from the mean for British monarchs after corona- tion?

Explanation / Answer

(A) H0 : popes = k&Q

Ha : popes   k&Q

(B) Here confidence interval = 1 - 0.01 = 99% so we would evaluate the 99% confidence interva.

here means for popes  xpopes = 13.125

standard deviation of sample for popes s1 = 8.96

Sample size n1 = 24

mean for kings & queen xkings & queen= 22.7143

standard deviation of sample for popes s2 = 18.603

sample size n2 = 14

standard error of differnece sed = sqrt [s12 /n1 + s22 /n2] = sqrt [8.962 /24 + 18.6032 /14] = 5.2975

Here ration bettween stadnard deviation is more than 2 so we use t test for unequal variances

t = (M1 -M2)/ se0 = (22.7143 - 13.125)/ 5.2975 = 1.81

so here degree of freedom dF = 16 and alpa = 0.01

Confidence interval = (xpopes -  xkings & queen)+- t16,0.01 se0

= (22..7143 - 13.125) +- 2.9208 * 5.2975

= 9.5893 +- 15.4729

= (-5.8836, 25.0622)

Conclusion : Here we will fail to reject the null hypothesis.

(c) Here, there is not sufficient evidece to support the claim that the mean longevity for popes is different from the mean for British monarchs after coronations.

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