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Amanda [17]
3 years ago
6

Hoping to attract more shoppers, a city builds a new public parking garage downtown. The city plans to pay for the structure thr

ough parking fees. The consultant, who advised the city on this project, randomly selected 44 weekdays. Daily fees collected averaged $126. Based on data from other parking structures, the consultant will assume parking fees at this parking garage are Normally distributed with a standard deviation of $15. If a 95% confidence interval was constructed, how would the margin of error compare to one used to create a 90% confidence interval
Mathematics
1 answer:
posledela3 years ago
6 0

Answer:

MOE_{95} = 1.192\cdot MOE_{90}

Step-by-step explanation:

The margin of error is computed using the formula:

MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}

The critical of <em>z</em> for 95% confidence level and 90% confidence level are:

z_{0.05/2}=z_{0.025}=1.96\\\\z_{0.10/2}=z_{0.05}=1.645

*Use a <em>z</em>-table.

The sample size is n = 44.

Compare the MOE for 95% confidence level and 90% confidence level as follows:

\frac{MOE_{95}}{MOE_{90}}=\frac{1.96\times (15/\sqrt{44})}{1.645\times (15/\sqrt{44})}

\frac{MOE_{95}}{MOE_{90}}=\frac{1.96}{1.645}\\\\\frac{MOE_{95}}{MOE_{90}}=1.192\\\\MOE_{95} = 1.192\cdot MOE_{90}

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Complete Question

In your biology class, your final  grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 25% of your total grade, each major test is worth 22:5%, and the final exam is worth 30%. Compute the weighted average for the following scores: 92 on the lab, 81 on the first major test, 93 on the second major test, and 85 on the final exam. (Enter your answer to one decimal place)

Answer:

The weighted average is  W = 87.65

Step-by-step explanation:

From the question we are told that

  The worth of the lab score is  25% of total grade

  The worth of each major  test is   22.5% of total grade

   The worth of final exam is  30% of total grade

The  score on lab is  92

The score on first major test 81

The score on second major test 93

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Generally the weighted score is mathematically represented as

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=> W = 0.25 *  92 + 0.225* 81 + 0.225* 93 +0.30 * 85

=> W = 87.65

   

   

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