Question

Sundrop candies inc claims that their 3 oz bag of candies contains 90 pieces of candy. A consumer group does not think this claim is accurate and obtains a random sample of 26, 3oz bags of the Sundrop candies. The number of candies in each bag is recorded:

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

a) Find a 95% confidence interval for the mean of candies contained the 3oz bag of Sundrop candies.

b) Check if the normality assumptions are met.

c) What is the 95% confidence interval for the mean number of candies in a 3oz bag of Sundrop candies? Round to 3 decimal places.  ≤ μ ≤ . Interpret the confidence interval that you obtained.

d) What can be said about the Sundrop candies' claim that their 3oz bag of candies contains over 90 pieces of candy (reference confidence interval)?

Answer 1

A)

As the population s.d is unknown we will use t distribution to estimate the interval

N = 26

Mean = 88.58

S.d = 2.19

Degrees of freedom is = n-1 = 25

For 25 degrees of freedom and 95% confidence level critical value t from t table is = 2.06

Margin of error (MOE) = t*s.d/√n = 2.06*88.58/√26 = 1.1754

Confidence interval is given by

(Mean -MOE, Mean + MOE)

[87.4046, 89.7554].

B)

Yes met as the sample is random

C)

87.405 < u < 89.755

D)

Null hypothesis Ho : u = 90

Alternate hypothesis Ha : u > 90

As the interval do not contain 90 in it we reject the null hypothesis Ho