Got Milk According to the U.S. Department of Agriculture, 58.8% of males between

Question

Got Milk

According to the U.S. Department of Agriculture, 58.8% of males between 20 and 39 years old consume the minimum daily requirement of calcium. After an aggressive “Got milk” advertising campaign, the USDA conducted a survey of 55 randomly selected males between the ages of 20 and 39 and found that 36 of them consume the recommended daily allowance of calcium.

A)Construct a 95% confidence interval to estimate the population proportion of males that consume the minimum daily requirement of calcium. Please do this “by hand” using the formula and showing your work (please type your work, no images accepted here). Then, verify your result using Stat à Proportions Stats à One Sample à With Summary. Copy and paste your StatCrunch result in your document as well.

B)At the a = 0.05, is there evidence to conclude that the percentage of males between the ages of 20 and 39 who consume the recommended daily allowance of calcium has changed? Conduct a full hypothesis test by following the steps below. Enter an answer for each of these steps in your document.

1)State the null and alternative hypotheses using correct notation.

2)State the significance level for this problem.

3)Check the three conditions of the Central Limit Theorem that allow you to use the standard Normal test statistic using one complete sentence for each condition. Show work for the numerical calculation.

4)Calculate the test statistic “by-hand.” Show the work necessary to obtain the value by typing your work and provide the resulting test statistic.

5)Calculate the p-value using the standard Normal table and provide the answer.

6)State whether you reject or do not reject the null hypothesis and your reason for your answer in one sentence.

7)State your conclusion in context of the problem (i.e. interpret your results and/or answer the question being posed) in one or two complete sentences.

8)Use StatCrunch (Stat à Proportion Stats à One Sample à with Summary) to verify your test statistic and p-value. Copy and paste this box into your document.

C)Explain the connection between the confidence interval and the hypothesis test in this problem (discuss this in relation to the decision made from your hypothesis test). Answer this question in one to two sentences.

Explanation / Answer

PART A.
given that,
possibile chances (x)=36
sample size(n)=55
success rate ( p )= x/n = 0.6545
CI = confidence interval
confidence interval = [ 0.6545 ± 1.96 * Sqrt ( (0.6545*0.3455) /55) ) ]
= [0.6545 - 1.96 * Sqrt ( (0.6545*0.3455) /55) , 0.6545 + 1.96 * Sqrt ( (0.6545*0.3455) /55) ]
= [0.5289 , 0.7802]
-----------------------------------------------------------------------------------------------
interpretations:
1. We are 95% sure that the interval [ 0.5289 , 0.7802] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population proportion

PART B.
Given that,
possibile chances (x)=36
sample size(n)=55
success rate ( p )= x/n = 0.6545
success probability,( po )=0.588
failure probability,( qo) = 0.412
null, Ho:p=0.588  
alternate, H1: p!=0.588
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.65455-0.588/(sqrt(0.242256)/55)
zo =1.0027
| zo | =1.0027
critical value
the value of |z | at los 0.05% is 1.96
we got |zo| =1.003 & | z | =1.96
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 1.00268 ) = 0.31602
hence value of p0.05 < 0.316,here we do not reject Ho
ANSWERS
---------------
null, Ho:p=0.588
alternate, H1: p!=0.588
test statistic: 1.0027
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.31602

we dont have evidnce that ,At the a = 0.05, is there evidence to conclude that the percentage of males between the ages of 20 and 39 who consume the recommended daily allowance of calcium has changed.

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