Keri is the owner of a new restaurant in the downtown area of her hometown. To c
ID: 2651955 • Letter: K
Question
Keri is the owner of a new restaurant in the downtown area of her hometown. To continuously improve service, she would like to know if completed dishes are being delivered to the customer’s table within one minute of being completed by the chef. A random sample of 75 completed dishes showed that 60 were delivered within one minute of completion.
Calculate the 90%, 95%, and 99% confidence interval for the true population proportion. Interpret your response within the context of the situation. Refer to Chapter 17, pp. 427-430 on calculating confidence intervals. Click here for Table A.2 from the appendix.
Explanation / Answer
Answer:
1. Identify the population of interest and define the parameter of interest being estimated.
The population of interest is the dishes that are being served at this chain of restaurants.
p= the population proportion of dishes that are served with in one minute of completion.
p=60/75=0.8= the sample proportion of dishes that are served within one minute of completion.
n=75 is the sample size.
Calculate the confidence interval.
At a 95% CI, the critical value is z*=1.96.
This value is found on the last row of the t-distribution table
=0.8 ± 1.960*[square root of (0.8(1-0.8))/ 75]
=(0.709,0.891)
Interpretation:
We are 95% confident that the true proportion of dishes that are served within one minute of completion for this chain of restaurants is between 0.709 and 0.891.
At 90% confidence level= Mean ±1.645 standard deviation/square root of n
=0.8 ± 1.645*[square root of (0.8(1-0.8))/ 75]
=(0.724,0.876)
Interpretation:
We are 90% confident that the true proportion of dishes that are served within one minute of completion for this chain of restaurants is between 0.724 and 0.876.
At 99% confidence level= Mean ±2.576 standard deviation/square root of n
=0.8 ± 2.576*[square root of (0.8(1-0.8))/ 75]
=(0.681,0.919)
Interpretation:
We are 99% confident that the true proportion of dishes that are served within one minute of completion for this chain of restaurants is between 0.681 and 0.919.
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