Question

Tallula's Toy Factory has a plant in Elginfield, Ontario where they manufacture glass marbles. The marbles are packed in mesh bags for sale under the brand name Elgin Marbles. The masses of the bags are known to be normally distributed. A random sample of 65 bags yields an average mass of 0.635 kg with a standard deviation of 0.076 kg. Find a 99% two-sided confidence interval on the population mean mass in kg. State the value of the upper-confidence limit for the two-sided confidence interval. Express your answer to three decimal places.

Answer 1

Since , the sample standard deviation is not known.

Therefore , use t-distribution.

Now , df=degrees of freedom=n-1=65-1=64

The critical value is , $t_{df,\alpha/2}=t_{64,0.01/2}=2.655$ ; The Excel function is , =TINV(0.01,64)

Therefore , the 99% tow-sided confidence interval on the population mean mass in kg is ,

$0.635\pm 2.655*\frac{0.076}{\sqrt{65}}$

$0.635\pm 0.025$

The upper-confidence limit for the two-sided confidence interval is 0.660

Answer 2

Since , the sample standard deviation is not known.

Therefore , use t-distribution.

Now , df=degrees of freedom=n-1=65-1=64

The critical value is , $t_{df,\alpha/2}=t_{64,0.01/2}=2.655$ ; The Excel function is , =TINV(0.01,64)

Therefore , the 99% tow-sided confidence interval on the population mean mass in kg is ,

S X = tdf, 0/2 n

$0.635\pm 2.655*\frac{0.076}{\sqrt{65}}$

$0.635\pm 0.025$

The upper-confidence limit for the two-sided confidence interval is 0.660