Question

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14 A government watchdog association claims that 70% of people in the U.S. agree that the government is inefficient and wasteful. A government agency wants to test this claim. In a random sample of 1165 people in the U.S., 746 agreed with that view. At a 95% confidence level, is there enough evidence to reject the association's claim? is. A medical researcher says that at least 25% of U.S. adults are smokers. In a random sample of 200 U.S. adults, 24.5% say they are smokers. At a 99% confidence level, is there enough evidence to reject the researcher's claim?

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.7
Alternative Hypothesis, Ha: p ≠ 0.7

Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.6403 - 0.7)/sqrt(0.7*(1-0.7)/1165)
z = -4.45

P-value Approach
P-value = 0
As P-value < 0.05, reject the null hypothesis.

There is sufficient evidence to conclude the claim

2)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.25
Alternative Hypothesis, Ha: p < 0.25

Rejection Region
This is left tailed test, for α = 0.01
Critical value of z is -2.33.
Hence reject H0 if z < -2.33

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.245 - 0.25)/sqrt(0.25*(1-0.25)/200)
z = -0.16

P-value Approach
P-value = 0.4364
As P-value >= 0.01, fail to reject null hypothesis.

There is not sufficient evidence to conclude the claim