What is the percent decrease modeled in the function (picture)
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: 0.701
Step-by-step explanation:
Formula : , where
significance level ,
Population standard deviation, n= sample size.
As per given, n= 22
Critical z- value for 90% confidence level :
Then,
Hence , error bound (EBM) of the confidence interval with a 90% confidence level= ± 0.701