Question

In: Statistics and Probability

SCENARIO 4: I want to know the percentage of people who think gold is the best...

SCENARIO 4:
I want to know the percentage of people who think gold is the best color among all iPhone options. Anyone with a smartphone can answer. I want my margin of error to be +/- 3 percentage points. I want to use a z-value of 1.96.
1. Sample Size Formula to Use: [ answer here ]
2. Confidence Interval set to [ answer here ] because [explain why it is the right choice for this scenario] .
3. Margin of Error set to [ answer here ]because [explain why it is the right choice for this scenario] .
4. Variance set to [ answer here ] because [explain why it is the right choice for this scenario].
5. Optimal Sample Size = [insert number here]

Expert Solution

Suppose that percentage of people who think gold is the best color among all iphone options is 50% ( by defoult).

=0.5 ( proportion of people who think gold is the best color among all iPhone options).

Now given this quesion margin of error to be +/- 3 percentage points.

That is E=0.03, and z-value =1.96.

1) To find sample size (n), the formula is n = ,

n=, Sample size (n) = 1067.111 (it is fraction number, but sample size is whole number)

So that this fraction number is next to whole number.

The sample size (n)= 1068.

2) To set a confidance interval .

The formula is and z value= 1.96 it is 95% confidance level.

The confidance interval is (0.47, 53).

It is right choice, because the percantage of people who think gold is the best color among all iphone options is 50%, (0.5) lies between this confidance interval means that 95% people lies between this interval.

3) The marginal error is increase then sample size is decreases and sample size decreases than confidance intereval also increase.

4) The variance this scenario basicaly used to p*(1-q)/n, becasue that n1068 > 30 and follows to normal.

the variance is 0.5*0.5/1068 = 0.000234.

5) And optimal sample size is 1068.

orchestra answered 1 year ago

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