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000 AT&T; LTE 1:25 PM 99% mathxl.com Wes Shop Youn. Welcome t... Ims.ssc.ed... McGraw-H Ims.ssc.ed Homework Do Hom.. MTH 126-301, Fall 2017 Lisa Koscielski 11/2/17 1:25 PM Homework: Section 7.4 Homework Save Score: 2 of 4 pts 6 of 6 (6 complete) HW Score: 71.9%, 21.57 of 30 pts 7.4.61 i Question Help In a 2008 survey, people were asked their opinions on astrology-whether it was very scientific, somewhat scientfic, or not at all scientific. Of 1433 who responded 73 said astrology was very scientbific a. Find the proportion of people in the survey who belleve astrology is very sclentific b. Find à 95% confidence interval for the population proportion with this beset c. Suppose a TV news anchor said tat S% of people in the general population think astrology is very scenesc Would you say that is plausible? Explain your a. The proportion of people in the survey who believe astrology is very scientific is 0.0509 Round to four decimal places as needed.) b, Construct the 95% oonfidence interval for the population poportion wth the belieftut astoogy is very scientfic. (0.040.0.062)(Round to three decimal places as needed) c. Choose the correct answer below OA- 0 B C This is not plausible because 5% is inside he inerval. This is not plausible because 5% is outside the interval. This is plausble because 5% s outside the interval. D This is plausble because 5% is inside the interval. Question is complete. Tap on the red indicators to see incorrect answers Simlar Question

Explanation / Answer

Solution:

Part a

We are given

n = 1433

x = 73

Sample proportion = P = x/n = 73/1433 = 0.050942

Required proportion = 0.0509

Part b

Here, we have to find 95% confidence interval for population proportion.

Formula for confidence interval is given as below:

Confidence interval = P -/+ Z*sqrt[P(1 – P)/n]

Where Z is critical value for 95% confidence level

Z = 1.96

(By using z-table)

Confidence interval = 0.05094208 -/+ 1.96*sqrt[0.05094208*( 1 - 0.05094208) / 1433]

Confidence interval = 0.05094208 -/+ 1.96* 0.0058

Confidence interval = 0.05094208 -/+ 0.0114

Lower limit = 0.05094208 - 0.0114 = 0.040

Upper limit = 0.05094208 + 0.0114 = 0.062

Confidence interval = (0.040, 0.062)

Part c

Correct answer:

This is plausible because 5% is inside the interval.

(It is observed that 5% or 0.05 is lies within confidence interval (0.040, 0.062)).

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