a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: ? Select an answer ♥ |(please enter a decimal) H1: ? v Select an answer (Please enter a decimal) c. The test statistic ? v |(please show your answer to 3 decimal places.)

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You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly smaller than 68% at a level of significance of \( \alpha = 0.01 \). According to your sample, 31 out of 53 potential voters prefer the Democratic candidate.

a. For this study, we should use \( \text{Select an answer} \)

b. The null and alternative hypotheses would be:

   \( H_0: \; ? \; \text{Select an answer} \) (please enter a decimal)

   \( H_1: \; ? \; \text{Select an answer} \) (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 \( ? \; \alpha \)

f. Based on this, we should \( \text{Select an answer} \) the null hypothesis.

g. Thus, the final conclusion is that…

- \( \bigcirc \) The data suggest the population proportion is not significantly smaller than 68% at \( \alpha = 0.01 \), so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 68%.

- \( \bigcirc \) The data suggest that the population proportion is not significantly smaller than 68% at \( \alpha = 0.01 \), so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 68%. 

- \( \bigcirc \) The data suggest the population proportion is significantly smaller than 68% at \( \alpha = 0.01 \), so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 68%.

h. Interpret the p-value in the context of the study.

- \( \bigcirc \) If the sample proportion of voters who prefer the Democratic candidate is 59% and if another 53 voters are surveyed then there would be a 6.89% chance of concluding that fewer than 68% of all voters surveyed prefer the Democratic candidate.

- \( \bigcirc \) There is a 6.89% chance that fewer than 68% of all voters prefer the Democratic candidate.

- \(
Transcribed Image Text:You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly smaller than 68% at a level of significance of \( \alpha = 0.01 \). According to your sample, 31 out of 53 potential voters prefer the Democratic candidate. a. For this study, we should use \( \text{Select an answer} \) b. The null and alternative hypotheses would be: \( H_0: \; ? \; \text{Select an answer} \) (please enter a decimal) \( H_1: \; ? \; \text{Select an answer} \) (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 \( ? \; \alpha \) f. Based on this, we should \( \text{Select an answer} \) the null hypothesis. g. Thus, the final conclusion is that… - \( \bigcirc \) The data suggest the population proportion is not significantly smaller than 68% at \( \alpha = 0.01 \), so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 68%. - \( \bigcirc \) The data suggest that the population proportion is not significantly smaller than 68% at \( \alpha = 0.01 \), so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 68%. - \( \bigcirc \) The data suggest the population proportion is significantly smaller than 68% at \( \alpha = 0.01 \), so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 68%. h. Interpret the p-value in the context of the study. - \( \bigcirc \) If the sample proportion of voters who prefer the Democratic candidate is 59% and if another 53 voters are surveyed then there would be a 6.89% chance of concluding that fewer than 68% of all voters surveyed prefer the Democratic candidate. - \( \bigcirc \) There is a 6.89% chance that fewer than 68% of all voters prefer the Democratic candidate. - \(
Expert Solution
Step 1

Given : n=53 , X=31 , p0=0.68 , α=0.01

The estimate of the sample proportion is ,

p-hat=X/n=31/53=0.5849

Our aim is to answer the following (a) , (b) and (c)

As per our guidelines, we are supposed to answer only 3 sub-parts and rest can be reposted.

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