Question

You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly different from 51% at a level of significance of a -0.01. According to your sample, 37 out of 74 potential voters prefer the Democratic candidate a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: ? ? please enter a decimal) (Please enter a decimal) c. The test statistic (please show your answer to 3 decimal places.) d. The p-value- (Please show your answer to 4 decimal places.) e. The p-value is ? f. Based on this, we should Select an answer the mull hypothesis. 3. Thus, the final conclusion is that... The data suggest the populaton proportion is significantly different from 51% at a=0.01. so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 51% The data suggest the population proportion is not significantly different from 51% at a=0.01. so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 51% The data suggest the population proportion is not significantly different from 51% at a -0.01, 50 there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 51% h. Interpret the p-value in the context of the study. There is a 86.34% chance of a Type I error. There is a 86.34% chance that the percent of all voters who prefer the Democratic candidate differs from 51% If the population proportion of voters who prefer the Democratic candidate is 51% and if another 74 voters are surveyed then there would be a 86.34% chance that either fewer than 50% of the 74 voters surveyed prefer the Democratic candidate or more than 52% of the 74 voters surveyed prefer the Democratic candidate If the sample proportion of voters who prefer the Democratic candidate is 50% and if another 74 voters are surveyed then there would be a 86.34% chance that we would conclude either fewer than 51% of all voters prefer the Democratic candidate or more than 51% of all voters prefer the Democratic candidate. i. Interpret the level of significance in the context of the study If the population proportion of voters who prefer the Democratie candidate is 51% and if another 74 voters are surveyed then there would be a 1% chance that we would end up falsely concuding that the proportion of voters who prefer the Democratic candidate is different from 5196 There is a 1% chance that the proportion of voters who prefer the Democratic candidate is different from 519 If the proportion of voters who prefer the Democratic candidate is different from 51% and if another 74 voters are surveyed then there would be a 19 chance that we would end up falsely concuding that the proportion of voters who prefer the Democratic candidate is equal to 51% There is a 1% chance that the earth is flat and we never actually sent a man to the moon.

Answer 1

n = 74

x =37

p̄ = x/n = 0.5

α = 0.01

a) for this study we should use one proportion z test

b) Null and Alternative hypothesis:

Ho : p = 0.51

H1 : p ≠ 0.51

c) Test statistic:

z = (p̄ -p)/√(p*(1-p)/n) = (0.5 - 0.51)/√(0.51 * 0.49/74) =-0.1720

#the test statistics =Z= -0.172

d) p-value = P(|Z|>0.1721)

= 2*P(Z>0.1721)  

value of z is obtain from standard normal table

=2*0.4317

=0.8634

P-value =0.8634

e) p-value > α,

f) Do not reject the null hypothesis

g) Conclusion:

The data suggest the population proportion is not significantly different from 51% at 0.05 , so there is not sufficient evidence  to conclude that the proportion of voters who prefer the Democratic candidate is different from 51%

Option c is correct

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