Quiz 5 Name To assess the accuracy of a thermostat, the temperature reading on t
ID: 3376622 • Letter: Q
Question
Quiz 5 Name To assess the accuracy of a thermostat, the temperature reading on the thermometer is repeatedly recorded a total of 20 times and the sample mean is computed to be 97.0 °F. Suppose the thermostat readings are normally distributed with unknown mean ? and known standard deviation ?-12-F I. Give a point estimate of ? 2. What is the standard error of the estimate above? 3. Find the 95% C.1. for fl and write down the margin of error for the C.L. 4. Choose the correct option (T-True, F- False, I-Indeterminate) for each claim below: F F TF 1 1 97.5 is a reasonable guess for ? at 0.95 confidence level 97.5 °F is a reasonable guess for ? at 0.90 confidence level belongs to the C.I. in Part 3 with probability 0.95 belongs to the C.I. in Part 3 with probability 1.00 TF 5. To decrease the margin of error found in Part 3, what can you do? Check all options that app O Decrease confidence level O Decrease sample size O Increase confidence level Increase sample size Decrease measurement error O Increase measurement error 6. How large should n be so that a 95% CI, for ? will have a margin of error 0.2 ? What does the "95%" in Part 6 mean?Explanation / Answer
Solution1:
point estiamte of mu is xbar=97
Solution2:
standard error of mean=population standard deviation/sqrt(sample size)
=1.2/sqrt(20)
=0.268
Soluton3:
95% confidence interaval for mean=
point estimate-margin of error,point estimate+margin of error
margin of error=Z crir*pop sd/sqrt(sample size)
Z crit for 95%=1.96
margin of error=1.96*1.2/sqrt(20)
=0.5259
therfore 95% confidence interval for mean is
97-0.5259,97+0.5259
96.4741,97.5259
lower limit=96.4741
upper limit=97.5259
we are 95% confident that the true population mean lies in between
96.4741 and 97.5259
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