7. Step 1: To assess the accuracy of a laboratory scale, a standard weight known

Question

7.

Step 1: To assess the accuracy of a laboratory scale, a standard weight known to weigh 10 grams is weighed repeatedly. The scale readings are Normally distributed with unknown mean (this mean is 10 grams if the scale has no bias). The standard deviation of the scale readings is known to be 0.0002 gram. The weight is measured five times. The mean result is 10.0023 grams. What is the 98% confidence interval for the mean of repeated measurements of the weight? O 9.5022.10 5024 grams. O (9.9998, 10.0002 grams. O (10.0019, 10.0027 grams. O 0.0021,10 grams. 10.0025 Step 2: To assess the accuracy of a laboratory scale, a standard weight known to weigh 10 grams is weighed repeatedly. The scale readings are Normally distributed with unknown mean (this mean is 10 grams if the scale has no bias). The standard deviation of the scale readings is known to be 0.0002 gram. How many measurements must be averaged to get a margin of error of t0.0001 grams with 98% confidence? 75 22 O 53

Explanation / Answer

6. 1. Here n=5 so we will use t distribution t=3.747 for 4 df at 98% CI

Mean=10.0023 and sd=0.0002

So Margin of error=t*sd/sqrt(n)=0.0004

Hence CI=mean+/-E=10.0023+/-0.0004=(10.0019,10.0027)

2. z value for 98% CI is 2.33

Now E=0.0001

Formula for E=z*sd/(sqrt(n)

so n=(z*sd/E)^2=21.7=22

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