# 2023 There is 98 chance that the true population mean is within the interval 13 11 15 49 0 lower limit upper

2023 There is 98 chance that the true population mean is within the interval 13 11 15 49 0 lower limit upper

There is 98% chance that the true population mean is within the interval (13.11, 15.49)

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lower limit

upper limitGive a brief interpretation of the meaning of the confidence interval you have found.

We are 5% confident that the true proportion of actors who are extroverts falls above this interval.

We are 95% confident that the true proportion of actors who are extroverts falls within this interval.

We are 5% confident that the true proportion of actors who are extroverts falls within this interval.

We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.(c) Do you think the conditions n·p > 5 and n·q > 5 are satisfied in this problem? Explain why this would be an important consideration.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.

(a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 95% confidence interval for p. (Round your answers to two decimal places.)

(c) Do you think the conditions n·p > 5 and n·q > 5 are satisfied in this problem? Explain why this would be an important consideration.

Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). This condition is associated with an average total calcium level below 6 mg/dl. Recently, the patient’s total calcium tests gave the following readings (in mg/dl). Assume that the population of x values has an approximately normal distribution.

9.9 9.4 10.3 8.5 9.4 9.8 10.0 9.9 11.2 12.1

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean reading x bar and the sample standard deviation s. (in mg/dl; round your answers to two decimal places.)

(b) Find a 99.9% confidence interval for the population mean of total calcium in this patient’s blood. (in mg/dl; round your answer to two decimal places.)

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 44 farming regions gave a sample mean of x bar = \$6.88 per 100 pounds of watermelon. Assume that σ is known to be \$1.94 per 100 pounds.

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop (in dollars). What is the margin of error (in dollars)? (For each answer, enter a number. Round your answers to two decimal places.)

(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.27 for the mean price per 100 pounds of watermelon. (Enter a number. Round up to the nearest whole number.)

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.(a) Suppose n = 43 and p = 0.37. (For each answer, enter a number. Use 2 decimal places.)n·p = 15.91n·q = 27.09Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)_____, p̂ _____ be approximated by a normal random variable because _____ _____.first blankYesNo second blankcancannot third blankn·q does not exceedn·p exceeds n·q exceedsn·p and n·q do not exceedboth n·p and n·q exceedn·p does not exceedfourth blank (Enter an exact number.) 10What are the values of μp̂ and σp̂? (For each answer, enter a number. Use 3 decimal places.)μp̂ = mu sub p hat = 15.91σp̂ = sigma sub p hat = 3.166

(b) Suppose n = 25 and p = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

(c) Suppose n = 56 and p = 0.27. (For each answer, enter a number. Use 2 decimal places.)

Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

What are the values of μp̂ and σp̂? (For each answer, enter a number. Use 3 decimal places.)

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