A sample of 10 individuals from Population-l gives a sample standard deviation o

Question

A sample of 10 individuals from Population-l gives a sample standard deviation of 0.231. A similar sample of size 12 from Population-2 gives a corresponding value of 0.331.Choose the correct statement. The two populations' standard deviations are same at 5% level: the two populations' standard deviations are different at 10% level: The two populations' standard deviations are not same at 1% level: all the above statements are correct: none of the above is correct. You have measured the systolic blood pressure of a random sample of 25 employees of a company. A 95% confidence interval for the mean systolic blood pressure for the employees is computed to be (122, 138). Which of the following statements gives a valid interpretation of this interval? If the sampling procedure were repeated many times, then approximately 95% of the resulting confidence intervals would contain the mean systolic blood pressure for employees in the company About 95% of the employees in the company have a systolic blood pressure between 122 and 138. If the sampling procedure were repeated many times, then approximately 95% of the sample means would be between 122 and 138. The probability that the sample mean falls between 122 and 138 is equal to 0.95. In the past decade there had been extensive antismoking campaigns to try and reduce the proportion of smokers in the population. In 1982, a survey of 350 adult females revealed that 148 smoked. In 2009, 488 adult females were surveyed and 163 smoked. Suppose the p-value was found to be 053. This means: There is some, but not overwhelming evidence, that the proportion of smokers has decreased. The probability that the proportion of smokers has not changed is 0.053. The proportion of smokers has definitely decreased. There is no evidence that the proportion of smokers is the same in both years. There is overwhelming evidence that the proportion of smokers has stayed the same. While testing a null hypothesis against an alternative hypothesis, the P-value implies: (a) the probability that the null hypothesis is coming true when it is actually false: (b) assuming that the null true, it is the probability of observing the given data (or more extreme data): (c) assuming that the null hypothesis is true, it is the probability of the alternative hypothesis coming true: (d) It is the probability of rejecting the null when the alternative is correct: (e) none of the above statements is true. While finding a confidence interval (CI) of the population mean (mu) with known standard deviation, the CI (choose one) shrinks as the confidence level goes up: shrinks as the sample size goes up: shrinks as the population std (sigma) goes up: all of the above three are correct: none of the above three (a, b, c) is correct

Explanation / Answer

10) n1 = 10 ,s1 =0.231

n2 = 12 , s2 = 0.331

test Statistic = s1^2/s2^2 = 0.231^2 / 0.331^2 = 0.48704374

df1 =n1-1 = 9

df2 = n2 -1 = 11

P(F < 0.48704374 ) = 0.14

p-value =2min(0.14,0.86) = 0.28

if p-value is more than alpha ,we fail to reject the null

and hence

option A) is correct

as 0.28 > 0.05

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