The Arizona Department of Transportation wishes to survey state residents to determine what proportion of the population would like to increase statewide highway speed to 75 from 65 mph. At least how many residents do they need to survey if they want to be at least 99% confident that the sample proportion is within 0.07 of the true proportion?
Answers
Answer: 339
Step-by-step explanation:
Since the prior estimate of population proportion is unknown , then we take p= 0.5
Given : Margin of error : E=0.07
Critical value for 99% confidence interval :
Formula for sample size :-
Hence, the minimum sample size required = 339
i.e. they need to survey 339 residents.
Final answer:
To be at least 99% confident that the sample proportion is within 0.07 of the true proportion, the Arizona Department of Transportation needs to survey at least 753 residents.
Explanation:
To determine the minimum number of residents needed to survey in order to be at least 99% confident that the sample proportion is within 0.07 of the true proportion, we can use the formula:
n = (Zα/2)2p(1-p) / E2
Where:
- n is the required sample size
- Zα/2 is the critical value for the desired confidence level (in this case, 99% confidence)
- p is the estimated proportion (we assume 0.5 if no estimate is given)
- E is the maximum allowable error (in this case, 0.07)
Plugging in the values:
- Zα/2 = 2.576 (from the normal distribution table for a 99% confidence level)
- p = 0.5 (since no estimate is given)
- E = 0.07
Calculating n:
n = (2.576)2(0.5)(1-0.5) / (0.07)2 = 752.92
Rounding up to the nearest whole number, the Arizona Department of Transportation needs to survey at least 753 residents to be at least 99% confident that the sample proportion is within 0.07 of the true proportion.
Learn more about Sample Size Determination here:
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1. Let's review the information given to us to answer the question correctly:
Gaming system and equipment cost = $ 2,200
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2. What is the total amount of interest based on the APR?
Using Excel, we calculated the total number of months to pay the gaming system and the total interest, as you can read below.
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Step-by-step explanation:
I just did it and got it right. make sure to put $ or you will get it wrong