Question

2a) In a marketing campaign: A soda producer claims that 10% of all the soda bottles they continuously produce, have a winning message under the bottle cap ("winning caps"). Over a given three-month summer, during the soda producer's marketing campaign: You purchase 150 bottles of this soda, and collect the bottle caps in a bag without yet looking at them. To see if you should believe the soda producer's claim about the total proportion of winning caps, you decide to do a two-sided significance test, with an alpha-value of 1%. You then inspect all 150 of the bottle caps you've collected, and find that 6 of them are winning caps. In percentage form, and rounded to four digits past the decimal point: What is the approximate P-value of your test? Include a percentage symbol at the end of your numerical answer (with no spaces).

2b) Which of the following are correct general statements about the conclusion that you find from your significance test?

(Select all that apply. To be marked correct: All of the correct selections must be made, with no incorrect selections.)

	The P-value from your test, is less than or equal to your chosen alpha-value.
	Your sample results are not statistically significant.
	You reject the null hypothesis in favor of the two-sided alternative.
	Based upon the evidence from your significance test, you should no longer believe the null hypothesis claim.
	Your sample results are statistically significant.
	Based upon the evidence from your significance test, you have no reason to stop believing the null hypothesis claim.
	The P-value from your test, is greater than your chosen alpha-value.
	You fail to reject the null hypothesis.

Answer 1

a)

Ho :   p =    0.1                  
H1 :   p ╪   0.1       (Two tail test)          
                          
Level of Significance,   α =    0.01                  
Number of Items of Interest,   x =   6                  
Sample Size,   n =    150                  
                          
Sample Proportion ,    p̂ = x/n =    0.0400                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.02449                  
Z Test Statistic = ( p̂-p)/SE = (   0.0400   -   0.1   ) /   0.0245   =   -2.4495
                          

p-Value   =   0.0143   [excel formula =2*NORMSDIST(z)]              
Decision:   p value>α ,do not reject null hypothesis                       

b)

Your sample results are not statistically significant.

Based upon the evidence from your significance test, you have no reason to stop believing the null hypothesis claim.

The P-value from your test, is greater than your chosen alpha-value.

You fail to reject the null hypothesis.