Question

In 2005, 20% of all u.s. adults said that they had confidence in the u.s. congress to work in the best interest of the people of the united states. suppose that in 2015, in a random sample of 155 u.s. adults, 25 reported that they had confidence in the u.s. congress to work in the best interest of the people of the united states. does the sample provide evidence that the proportion of u.s. adults in 2015 who hold this view has decreased since 2005? test this claim at the 5% significance level. let p be the proportion of u.s. adults in 2015 who have confidence in the u.s. congress. use a significance level of α = 0.05 . assume all conditions hold. work is not required for this question. a) what are the null and alternative hypotheses?

Answer 1

The null hypothesis (H0): Proportion of U.S. adults with confidence in Congress in 2015 equals 2005 (p = 0.20). Alternative hypothesis (H1): Proportion in 2015 is less than 2005 (p < 0.20).

Null hypothesis (H0): The proportion of U.S. adults with confidence in the U.S. Congress in 2015 is the same as in 2005 (p = 0.20).

Alternative hypothesis (H1): The proportion of U.S. adults with confidence in the U.S. Congress in 2015 is less than in 2005 (p < 0.20).

At a 5% significance level (α = 0.05), if the p-value is less than 0.05, we reject the null hypothesis. This indicates evidence that the proportion of U.S. adults with confidence in the U.S. Congress has decreased since 2005.