Question

SunDrop Candies Inc claims that their 3 ounce bag of candies contains over 90 pieces of candy.

A consumer group does not think this claim is accurate and obtains a simple random sample of 26, 3 ounce, bags of the SunDrop Candies. The number of candies in each bag is recorded.

Find a 95% confidence interval for the mean number of candies contained in a 3 ounce bag of SunDrop Candies.

Here is the data:

total

89

90

84

89

91

90

87

86

93

89

89

86

87

90

89

89

90

91

88

88

87

86

91

86

86

92

2303

a) Check that the normality assumptions are met.

b) What is the 95% confidence interval for the mean number of candies in a 3 ounce bag of SunDrop Candies? Round to 3 decimal places
____≤ μ ≤____

c) Interpret the confidence interval obtained in previous question.

d) What can be said about the SunDrop Candies' claim that their 3 ounce bag of candies contains over 90 pieces of candy? Be complete in your explaination. You should reference your confidence interval.

Answer 1

a) The sample is reasonable random and standard deviation is known. Moreover the sample size is closer to 30 as well so normality assumptions are met
Since we know that

Where n is the number of data points
Now

and n = 26
This implies that

Since we know that

b) Mean () = 88.5769
Sample size (n) = 26
Standard deviation (s) = 2.194
Confidence interval(in %) = 95

Since we know that

Required confidence interval =
Required confidence interval = (88.5769-0.8859, 88.5769+0.8859)
Required confidence interval = (87.691, 89.4628)

c) There is a 95% chances that the true mean of the population is between 87.691 and 89.4628

d) Since 90 doesn't belong in the confidence interval (87.691, 89.4628) which have 0.95 probability of having true mean, so there is less chances that the claim that their 3 ounce bag of candies contains over 90 pieces of candy of happening.
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