How to solve -2 2/5 subtract 7/10 How to solve -3 subtract 1/10
2 answers:
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Answer:
1) z = -6.32
2) p-value = 0.001 × 10^(-2)
3) we will reject the null hypothesis and conclude that there is enough evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court
Step-by-step explanation:
We are told that In a representative sample of 1000 adult Americans, only 400 could name at least one justice.
Thus:
Sample proportion; p^ = 400/1000 = 0.4
Sample size: n = 1000
We want to find if there is convincing evidence to support the claim that fewer than half of adult Americans can name at least one justice.
Thus, the hypothesis is defined as;
Null hypothesis:H0: p ≥ 0.5
Alternative hypothesis: Ha < 0.5
Formula for the test statistic is;
z = (p^ - p)/√(p(1 - p)/n)
Plugging in the relevant values;
z = (0.4 - 0.5)/√(0.5(1 - 0.5)/1000)
z = -6.32
From online p-value from z-score calculator attached, using z = -6.32; significance level of 0.01; one tailed hypothesis;
We have:
p-value = 0.00001 = 0.001 × 10^(-2)
The p-value is less than the significance level and so we will reject the null hypothesis and conclude that there is enough evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court
Answer:
Step-by-step explanation:
The equation of a circle is given by:
Where (h, k) is the center and r is the radius.
The center of the circle is (1, -4).
And the radius is 3.
Substitute:
Simplify. Thus, our equation is: