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Suppose that the insurance companies did do a survey. They randomly surveyed 400drivers and found that 320claimed they always buckle up. We are interested in the population proportion of drivers who claim they always buckle up.

a. i. x = __________ ii. n = __________ iii. p鈥 = __________

b. Define the random variables Xand P', in words.

c. Which distribution should you use for this problem? Explain your choice.

d. Construct a 95%confidence interval for the population proportion who claim they always buckle up. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound.

e. If this survey were done by telephone, list three difficulties the companies might have in obtaining random results.

Short Answer

Expert verified

a). The quantity of successes is x=320.

The sample size is n=400drivers.

The purpose estimate for truth population proportion is p^=0.8.

b. stochastic variable Xis the amount of"{successes}"where drivers who claim they always buckle up.

p^is the percentage of drivers sampled who claim they always buckle up.

c. We use the conventional distribution N0.8,0.80.2400.

d. i) A 95%confidence interval for the population proportion is 0.761p0.839and EBM=0.039

ii)

Step by step solution

01

Successes  (a),(b) and (c)

a) - The whole number of successful attempts is x=320.

- There are n=400 drivers within the sample.

- The population mean percent information is p^=xn=320400=0.8

b) Component at unexpected times Average amount of "successes" inside which users claim to carry on tight is x.

The proportion of drivers polled who indicate their constantly buckle up is p^.

c) c) Given p^=0.8and n=400, the dispersion we must follow that compute a little is

N0.8,0.80.2400

02

Confidence Interval (d)

d) If the percent of sightings during a randomized subset n that relate to a category of things is p^, an estimate 100(1)% significance level here on proportion p of such populace that belong to the current group is .

p^z2p^(1p^)npp^+z2p^(1p^)n

localid="1649850739294" 2=10.952

localid="1649850746722" z2=1.96

localid="1649850753572" 0.81.960.8(10.8)400p0.8+1.960.8(10.8)400

localid="1649850761120" 0.80.039p0.8+0.039

localid="1649850768823" 0.761p0.839

This problem's graph is as follows:

03

Error bound

- The upper limit of the error limitation is

EBM=0.039

Is that if poll were conducted over the phone, the businesses might face three challengesin an exceedingly achieving random results:

- obtain results from people in a same town,

- obtain results from people of comparable ages,

- obtain inaccurate findings.

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