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In six packages of 鈥淭he Flintstones庐 Real Fruit Snacks鈥 there were five Bam-Bam snack pieces. The total number of snack pieces in the six bags was 68.We wish to calculate a 96%confidence interval for the population proportion of Bam-Bam snack pieces.

a. Define the random variables XandPin words.

b. Which distribution should you use for this problem? Explain your choice

c. Calculatep.

d. Construct a 96%confidence interval for the population proportion of Bam-Bam snack pieces per bag.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

e. Do you think that six packages of fruit snacks yield enough data to give accurate results? Why or why not?

Short Answer

Expert verified

(a) The sample of 68snack pieces for the proportion of Bam-Bam pieces is P',and the bag of snacks for the proportion of Bam-Bam snacks is X.

(b) From this we use normal distribution NPpqn.

(c) After calculate we get, p'=0.0735.

(d) The final result

1. we getCI=(0.00853,0.13853)

2.

3. Error bond mean EBM=0.0554.

(e) Almost certainly not.

Step by step solution

01

Explanation (a)

The sample of 68snack pieces for the proportion of Bam-Bam pieces is P', and the bag of snacks for the proportion of Bam-Bam snacks isX.

02

Explanation (b)

The problem is solved using the normal distribution. As we all know, the sample size for the population's standard deviation is greater than 30, and the distribution isNP,pqn.

03

Explanation (c)

In this we calculate p

By using formula

p'=5total number of smack pieces

by Computing,

p'=568

p'=0.0735.

04

Explanation (d)

i. The confidence interval should be stated.

The confidence interval's output,

n=58

CI=(0.00853,0.13853)

ii. The graph is as follows:

iii. The formula is used to compute the error bound.

EBM=z2p'q'n

EBM=20.0420.07350.926568

localid="1651847585804" EBM=0.0554

05

Explanation (e)

Do you believe that six packages of fruit snacks will provide enough data to provide accurate results, It's unlikely, because the samples were obtained using a basic random sample.

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Most popular questions from this chapter

Among various ethnic groups, the standard deviation of heights is known to be approximately three inches. We wish

to construct a 95% confidence interval for the mean height of male Swedes. Forty-eight male Swedes are surveyed. The

sample mean is 71 inches. The sample standard deviation is 2.8 inches.

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I. X=________

ii. 蟽 =________

iii. n =________

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Table 8.2shows a different random sampling of 20cell phone models. Use this data to calculate a 93% confidence interval for the true mean SAR for cellphones certified for use in the United States. As previously, assume that the population standard deviation is 蟽= 0.337.

Phone ModelSAR Phone ModelSAR
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Suppose average pizza delivery times are normally distributed with an unknown population mean and a population standard deviation of six minutes. A random sample of 28pizza delivery restaurants is taken and has a sample mean delivery time of 36minutes.

Find a 90% confidence interval estimate for the population mean delivery time.

Using the same p鈥 and level of confidence, suppose that n were increased to 100. Would the error bound become larger

or smaller? How do you know?

When designing a study to determine this population proportion, what is the minimum number you would need to survey to be 90% confident that the population proportion is estimated to within 0.05 ?

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