My Notes Ask Your In six packages of \"The Flintstonese Real Fruit Snacks\" ther

Question

My Notes Ask Your In six packages of "The Flintstonese Real Fruit Snacks" there were five Bam- Bam snack pieces. The total number of snack pieces in the six bags was 65. We wish to calculate a 96% confidence interval for the population proportion of Bam-Bam snack pieces. Part (a) Define the random variables X and Pin words. O X is the proportion of Bam-Bam snacks in a bag of snacks. P is the proportion of Bam-Bam pieces in a sample of 65 snack pieces. X is the proportion of Bam-Bam snacks in a sample of 65 snack pieces. Pis the proportion of Bam-Bam pieces in a bag of snacks. O X is the number of Bam-Bam snacks in a bag of snacks. P is the number of Bam- Bam pieces in a sample of 65 snack pieces. O X is the number of Bam-Bam snacks in a sample of 65 snack pieces. P is the proportion of Bam-Bam pieces in a bag of snacks. Part (b) Which distribution should you use for this problem? (Enter your answer in the form z or t where df is the degrees of freedom.) Explain your choice O The standard normal distribution should be used because we are interested in O The Student's t-distribution should be used because we do not know the standard deviation. O The Student's t-distribution should be used because 1o. which implies a small sample. O The binomial distribution should be used because the two outcomes are "Bam-Bam and "Not Bam-Bam Part (c) Calculate p: (Round your answer to three decimal places.) Part (d) Construct a 96% confidence interval for the population proportion of Bam-Bam snack pieces

Explanation / Answer

We should use a Z-ststistics i.e. distribution of Z i.e. a Normal distribution. We want to find C.I of p (the proportion of Bam Bam snack pieces in 6 packages. The sample value of p = p(hat) = 5/65.

Now by CLT, Z = [p(hat) - p ] / sqrt[ p(hat)(1-p(hat))/n ]follows a N(0,1) distribution. Using this distribution of Z which is the N(0,1) distribution we can calculate the 95% C.I.

So answer is Z-distribution.

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