4 -6 show work please 4. A corny dog manufacturer took a random sample of 25 dog

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4 -6 show work please

4. A corny dog manufacturer took a random sample of 25 dogs and found the average dog had 10 grams of fat with a variance of 16 squared grams. What are the 90% confidence limits of the average fat in all corny dog? a. 10 + 1.37 b. 10 + 1.96 c. 10 + 1.57 ( d. 10x1.37 e. Other 5. In a certain large town in Asia a random sample of 10 males out of 40 had a height of less than 6'. What are the 95% confidence limits of the true percentage of male inhabitants with heights below 6'? a. 5 + 15.5 b. 25 + 13.0 c. 25 + 13.4 d. 25 + 11.3 e. Other 6. Which of the following has no impact on the width of a confidence interval? a. A change in the mean b. A change in the sample size c. A change in the level of confidence (d. A change in the standard deviation e. None of these will affect the width of a confidence interval

Explanation / Answer

4. 90% conf level at 2 tail test has z value of -/+ 1.65 (use z table to find the same)

now using the eqn z=(X'-mu)/(sd/sqrt(n))

where n=25,sd=sqrt(variance)=sqrt(16) = 4 , mu=10

so., -/+ 1.65 = (X'-10)/(4/sqrt(25))

X'= 10 +/- 1.65*4/5 =10 +/- 1.32 approximately same as ans a&d

5.mu=mean %tage of people with less than 6 ft height = 10/40 =0.25 =25%

Since we are concerned with height less than 6ft it's a one tail test with z value as -1.64 (from the z table)

So., using the formuls

Z= (X'-mu)/(sd/sqrt(n)) we get

X'=mu - 1.64*sd/sqrt(n)

so., X' = 25 - 1.64 * sd/sqrt(n) now since we don't have sd of the population we won't be able to move further and so the ans is d) other

6) Change in the mean doesn't impact the width of the confidence interval since

the width is given as X'=mu +/- z* sd/sqrt(n) where mean mu is constant the only part which makes the confidence interval vary is z* sd/sqrt(n) where n is sample size, sd is std deviation and z is is the value derived from the level of confidence so ans is a change in mean

Hope the above explaination has helped you in understanding the problem Pls upvote the ans if it has really helped you. Good Luck!!

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