The population of North Carolina in 2010 was 9,535,483 people. The population of South Carolina in 2010 was 4,625,364 people.
2 answers:
a) North Carolina has 4,910,119 more people than South Carolina
b) the population of North Carolina is 2.06 times larger than that of South Carolina
Step-by-step explanation:
a)
Here the question is asking "how much larger is the population of North Carolina than South Carolina". This means that we have to compare the absolute value of the population of North Carolina with the population of South Caroline.
We have:
NC = 9,535,483 is the population of North Carolina
SC = 4,625,364 is the population of South Carolina
In order two compare the two, we have to calculated the difference between NC and SC. Plugging into a calculator, we get:
So, North Carolina has 4,910,119 more people than South Carolina.
b)
In this question, we are asked "how many times larger is North Carolina’s population than South Carolina’s population". This is equivalent to ask what is the ratio between the population of North Carolina to that of South Carolina.
As we said before, we have:
NC = 9,535,483 is the population of North Carolina
SC = 4,625,364 is the population of South Carolina
And by calculating the ratio, we find:
So, the population of North Carolina is 2.06 times larger than that of South Carolina.
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Answer:
A) Option C: H0: μ ≥ 7; HA: μ < 7
B) test statistic = -1.75
C) Option C: 0.025 ≤ p-value < 0.05
D) Option C: Do not reject H0 since the p-value is greater than α.
E) Option A: There is insufficient evidence to suggest that Americans sleep less than the recommended 7 hours of sleep.
Step-by-step explanation:
We are given;
Population mean; μ = 7
Sample mean; x = 6.7
Standard deviation; s = 2.1
Sample size; n = 150
A) Defining the hypothesis, we have;
Null Hypothesis; H0: μ ≥ 7
Alternative hypothesis; HA: μ < 7
B) Formula for the test statistic is;
z = (x - μ)/(s/√n)
Plugging in the relevant values, we have;
z = (6.7 - 7)/(2.1/√150)
z = -0.3/0.1715
z = -1.75
C) Using online p-value from z-score calculator attached with; z = - 1.75 ; α = 0.01 and one tailed distribution, we have;
The P-Value = 0.040059
Thus,the most appropriate answer is;
Option C: 0.025 ≤ p-value < 0.05
D) P-value is greater than the significance level, thus we fail to reject the null hypothesis.
E) We will conclude that there is insufficient evidence to suggest that Americans sleep less than the recommended 7 hours of sleep.
