Using the class data set, test the claim that the true proportion of blue m&m candies is 0.24 at the 0.05 confidence significance level. Null? Hypothesis?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.5: Interpreting Data
Problem 4E
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Using the class data set, test the claim that the true proportion of blue m&m candies is 0.24 at the 0.05 confidence significance level. Null? Hypothesis?

Hypothesis Test: Proportion One Sample
Alternative Hypothesis:
1) Population Proportion not = Claimed Proportion
0.05
Significance:
0.24
Claimed Proportion:
1816
Sample Size, n:
Number of Successes, x:
359
Evaluate
E Toggle Sample Editor
Results
Plot
Download
Сopy
Alternative Hypothesis:
p not equal p(hyp)
Sample Proportion:
0.19769
Test Statistic, z:
-4.22199
Critical z:
+1.95996
P-Value:
0.00002
95% Confidence Interval:
0.17937 <p < 0.21600
Transcribed Image Text:Hypothesis Test: Proportion One Sample Alternative Hypothesis: 1) Population Proportion not = Claimed Proportion 0.05 Significance: 0.24 Claimed Proportion: 1816 Sample Size, n: Number of Successes, x: 359 Evaluate E Toggle Sample Editor Results Plot Download Сopy Alternative Hypothesis: p not equal p(hyp) Sample Proportion: 0.19769 Test Statistic, z: -4.22199 Critical z: +1.95996 P-Value: 0.00002 95% Confidence Interval: 0.17937 <p < 0.21600
Expert Solution
Step 1

Z-test for one sample proportion : 

A z-test for one proportion is a hypothesis test that attempts to make a claim about the population proportion (p) for a certain population attribute. The test has null and the alternative hypothesis. The null hypothesis is a statement about the population proportion, which corresponds to the assumption of no effect, and the alternative hypothesis is the complementary hypothesis to the null hypothesis.   

Given :   

Sample size : n =  1816 

Number of success = 359 

Sample proportion : P^=xn=3591816=0.19770.20  

  • State null and alternative hypothesis : 

H0 : p = 0.24  

H1 : p  0.24  

Where, claimed proportion is p0 = 0.24 .  

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