Question

In: Statistics and Probability

Parameter Calculations A survey of 250 voters was conducted to determine who they would vote for...

Parameter Calculations

A survey of 250 voters was conducted to determine who they would vote for in an upcoming election for sheriff. Fifty-five percent said they would vote for Longmire.

What is the best unbiased estimate of the population proportion that will vote for Longmire (in other words, what is ?)
Find the margin of error E that corresponds to a 90% confidence Interval.
Construct the 90% confidence interval about the population proportion p.
Based on your results, can you conclude that Longmire will win the sheriff election?
What sample size would be required to estimate the true proportion of voters voting for Longmire within 3% at a 95% confidence level? Assume

The following are the batting averages of 16 randomly selected baseball players in MLB:

0.235

0.288

0.308

0.244

0.301

0.267

0.220

0.267

0.289

0.281

0.271

0.269

0.276

0.260

0.212

0.190

Calculate the mean and standard deviation of the batting averages.
Find the margin of error E that corresponds to a 95% confidence Interval.
Construct the 95% confidence interval about the population mean.
The current Twins average is 0.246 (Top 13 batters). Based on your confidence interval results, compare the Twins’ average to the estimated league average.
What sample size would be required to estimate the population mean within 0.05 at a 90% confidence level? (Use the sample standard deviation above to estimate the population standard deviation.)

Solutions

Expert Solution

Q-2. 16 randomly selected baseball players in MLB

(a)

Sample Standard Deviation, s	0.032936049145781
Variance (Sample Standard), s²	0.0010847833333333
Population Standard Deviation, ?	0.03189019245787
Variance (Population Standard), ?²	0.001016984375
Total Numbers, N	16
Sum:	4.178
Mean (Average):	0.261125
Standard Error of the Mean (SE_x?):	0.0082340122864454

(b) The margin of error shows the level of accuracy that a random sample of a given population has.

here no sample size given

If population and sample size same so margin of error is 0

where:

M = sample mean
Z = Z statistic determined by confidence level
s_M = standard error = ?(s²/n)

Calculation

M = 0.261125
t = 1.96
s_M = ?(0.03189²/16) = 0.01

? = M ± Z(s_M)
? = 0.261125 ± 1.96*0.01
? = 0.261125 ± 0.01562581

So [0.24549919, 0.27675081]

(d) 0.246 lie in this confidence interval

You can be 95% confident that the population mean (?) falls between 0.24549919 and 0.27675081.

(e) If population size is 16

So under these conditions sample size is also 16

orchestra answered 1 year ago

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