Question

A random sample of size n = 50 yielded p? = 0.40. a. Is the sample size large enough to use the large sample approximation to construct a confidence interval for p? Explain. b. Construct a 95% confidence interval for p. c. Interpret the 95% confidence interval. d. Explain what is meant by the phrase "95% confidence interval." a. Is the sample large enough? A. Yes, because n p? ? 15 and n q? ? 15. B. No, because n p? < 15 and n q? < 15. C. No, because n p? < 15 and n q? < 15. D. No, because n p? < 15 and n q? ? 15. b. The 95% confidence interval for p is ( , ). (Round to two decimal places as needed.)

          A random sample of size n = 50 yielded p? = 0.40.
a. Is the sample size large enough to use the large sample approximation to construct a confidence interval for p? Explain.
b. Construct a 95% confidence interval for p.
c. Interpret the 95% confidence interval.
d. Explain what is meant by the phrase "95% confidence interval."
a. Is the sample large enough?
A. Yes, because n p? ? 15 and n q? ? 15.
B. No, because n p? < 15 and n q? < 15.
C. No, because n p? < 15 and n q? < 15.
D. No, because n p? < 15 and n q? ? 15.
b. The 95% confidence interval for p is ( , ).
(Round to two decimal places as needed.)

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A random sample of size n = 50 yielded p? = 0.40.
a. Is the sample size large enough to use the large sample approximation to construct a confidence interval for p? Explain.
b. Construct a 95% confidence interval for p.
c. Interpret the 95% confidence interval.
d. Explain what is meant by the phrase "95% confidence interval."
a. Is the sample large enough?
A. Yes, because n p? ? 15 and n q? ? 15.
B. No, because n p? < 15 and n q? < 15.
C. No, because n p? < 15 and n q? < 15.
D. No, because n p? < 15 and n q? ? 15.
b. The 95% confidence interval for p is ( , ).
(Round to two decimal places as needed.)

Added by -Scar R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

04/30/2023

Step 1

We can do this by checking if np ≥ 15 and nq ≥ 15, where n is the sample size, p is the proportion of successes, and q is the proportion of failures (q = 1 - p). In this case, n = 50, p = 0.40, and q = 1 - p = 0.60. So, np = 50 * 0.40 = 20 and nq = 50 * 0.60 = Show more…

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A random sample of size n = 50 yielded p̂ = 0.40. a. Is the sample size large enough to use the large sample approximation to construct a confidence interval for p? Explain. b. Construct a 95% confidence interval for p. c. Interpret the 95% confidence interval. d. Explain what is meant by the phrase "95% confidence interval." a. Is the sample large enough? A. Yes, because n p̂ ≥ 15 and n q̂ ≥ 15. B. No, because n p̂ < 15 and n q̂ < 15. C. No, because n p̂ < 15 and n q̂ < 15. D. No, because n p̂ < 15 and n q̂ ≥ 15. b. The 95% confidence interval for p is ( , ). (Round to two decimal places as needed.)

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