Question

A pudding company has to ensure that they maintain strict oversight on the weight of a box of pudding they sell to their customers. Their advertisement states that the weight is between 290 and 310g per bottle of pudding. The company collected 15 bottles of pudding to measure their weight. The weight (gram) of each bottle are shown as follows. Use ?=0.0901

data: 306,290,289,309,289,307,301,307,302,298,295,295,291,289,296

Does the data suggest that the sample standard deviation in the weight per bottle compares to the hypothesised ?=43.9?

(a) Construct a 90.99% confidence interval estimate of the variance, σ2, of the weight per bottle

(b) What ?????????? needs to be satisfied for the inferences made in (a) to be valid? Use appropriate graph to check the normality assumption.

p-value =

(c) does the data above follow an approximately normal distribution?

(d) the data suggest that the standard deviation in weight (gram) per bottle is _____ 43.9?

[A] Significantly greater than

[B] Not significantly different from

[C] Significantly less than

Answer 1

(a)

Following table shows the calculations:

	X	(X-mean)^2
	306	70.56
	290	57.76
	289	73.96
	309	129.96
	289	73.96
	307	88.36
	301	11.56
	307	88.36
	302	19.36
	298	0.16
	295	6.76
	295	6.76
	291	43.56
	289	73.96
	296	2.56
Total	4464	747.6

Confidence interval:

(b)

Assumption: Data is normally distributed.

Followibg is the R script for normality test:

Following is the output

The p-value of the test is = 0.552

(c)

Yes since p-value is greater than 0.05 so we can assume that data is normally distributed. Box plot shows no outliers and it is almost symmetric so we can assume that data is normally distributed.

(d)

Since confidence interval contains 43.9 so correct option is

[B] Not significantly different from

Note: 43.9 should be variance not SD becuase sample data shows variance 53.4.