A poll of 1000 registered voters reveals that 480 of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 level of significance, do the data provide sufficient evidence to conclude that the percentage of voters who prefer the Democratic candidate is less than 50%? State the null hypothesis and the conclusion.

Question 1 options:

a) H0: p = 0.50; Do not reject H0.

b) H0: p = 0.50; Reject H0.

c) H0: p = 0.48; Do not reject H0.

d) H0: p = 0.48; Reject H0.

To test whether the percentage of voters who prefer the Democratic candidate is less than 50%, the null hypothesis (H0) should state that the proportion p is equal to 0.50.

H0: p = 0.50

To determine the conclusion based on the data, we need to perform a hypothesis test. The level of significance for the test is given as 0.05.

To conduct the hypothesis test, we can use a one-sample proportion test. We compare the observed proportion (480 out of 1000) with the hypothesized proportion of 0.50.

Using a statistical software, we can calculate the test statistic and p-value. If the p-value is less than 0.05, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

Without the specific values of the test statistic and p-value, we cannot determine the conclusion. Please provide the necessary statistical calculations or provide the test statistic and p-value for a definitive answer.

To determine if the data provides sufficient evidence to conclude that the percentage of voters who prefer the Democratic candidate is less than 50%, we need to conduct a hypothesis test.

The null hypothesis (H0) is the assumption that there is no significant difference and that the true proportion (p) of voters who prefer the Democratic candidate is equal to or greater than 50% (0.50). The alternative hypothesis (Ha) is the opposite of the null hypothesis, suggesting that the proportion is less than 50% (0.50).

In this case, the null hypothesis would be: H0: p = 0.50

To conduct the hypothesis test, we can use the Z-test for proportions. The formula for the test statistic (Z) is:
Z = (p - P) / sqrt(P*(1-P)/n)

Where:
p = proportion of voters who prefer the Democratic candidate in the sample (480/1000 = 0.48)
P = proportion assumed under the null hypothesis (0.50)
n = sample size (1000)

Calculating the test statistic, we find:
Z = (0.48 - 0.50) / sqrt(0.50*(1-0.50)/1000)

Now, we need to determine the critical value for the test statistic at a significance level of 0.05. This can be done using a Z-table or a statistical software. The critical value for a one-tailed test is -1.645.

If the test statistic (Z) is less than the critical value, we can reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis. Otherwise, if the test statistic is greater than or equal to the critical value, we fail to reject the null hypothesis.

Comparing the test statistic to the critical value, we find that Z is less than -1.645. Therefore, we reject the null hypothesis.

Therefore, the correct answer is:
d) H0: p = 0.48; Reject H0.