1 What Fdistribution value results from 10 degrees of freedo

1). What F-distribution value results from 10 degrees of freedom (numerator), 15 degrees if freedom (denominator) and area in the upper tail of the F-distribution equal to 0.05?

2). A soft drink bottle claims that the variance of all of the company\'s bottle is no more than 0.05 ounces. Which of the following is the appropriate null hypothesis for testing the claim?

3). The distribution used when testing a statement regarding a single population variance is the

4) The distribution used when testign a statement regarding the ratio of two population variances is the

5).Quality control officers of a ball bearing manufacturing plant measure the diameters of a sample of 20 manufactured ball bearings and the standard deviation of these measurements is found to be 0.09 inches

a.What is the 95% confidence interval for the variance in the diameters of the entire population of the manufacturer\'s ball bearings?

b. What is the 95% confidence interval for the standard deviation of the diameters of the entire population of the manufacturer\'s ball bearing?

6).Find X_0.95² with 40 degrees of freedom

Solution

1)

Using table/technology, if alpha = 0.05, df1 = 10, df2 = 15,

F(crit) = 2.54371855 [ANSWER]

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2)

The claim is always the alternative hypothesis, and the null hypothesis is always the opposite of the alternative.

Hence,

Claim (Ha): sigma^2 < 0.05

Thus,

Ho (null): sigma^2 >= 0.05 [ANSWER]

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3. Chi squared distribution.

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4. F distribution.

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5.

As              
              
df = n - 1 =    19          
alpha = (1 - confidence level)/2 =    0.025          
              
Then the critical values for chi^2 are              
              
chi^2(alpha/2) =    32.85232686          
chi^2(alpha/2) =    8.906516482          
              
Thus, as              
              
lower bound = (n - 1) s^2 / chi^2(alpha/2) =    0.0046846          
upper bound = (n - 1) s^2 / chi^2(1 - alpha/2) =    0.017279483          
              
Thus, the confidence interval for the variance is              
              
(   0.0046846   ,   0.017279483   ) [ANSWER, PART A]
              
Also, for the standard deviation, getting the square root of the bounds,              
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(   0.068444135   ,   0.131451447   )

[ANSWER, PART B]

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6.

For part 6, is the subscript a left tailed are aor right?

I will give both:

X(0.952, right tailed) = 26.3759903
X(0.952, left tailed) = 55.97837658

Please choose according to the convention of your class.

Using table or technology,