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MArishka [77]
2 years ago
8

State whether each of the following changes would make a confidence interval wider or narrower.​ (Assume that nothing else​ chan

ges.) a. Changing from a 95​% confidence level to a 99​% confidence level. b. Changing from a sample size of 15 to a sample size of 350. c. Changing from a standard deviation of 15 pounds to a standard deviation of 20 pounds.
Mathematics
1 answer:
Hatshy [7]2 years ago
3 0

Answer:

Step-by-step explanation:

The formula for determining confidence interval is expressed as

Confidence interval

= mean ± z × s/ √n

Where

z is the value of the z score

s = standard deviation

n = sample size

a) The 95​% confidence level has a z value of 1.96

The 99​% confidence level has a z value of 2.58

Since 99​% confidence level z value is greater than 95​% confidence level z value, if we input it into the formula, it will result to a higher confidence interval. So changing from a 95​% confidence level to a 99​% confidence level would make a confidence interval wider.

b) The √15 is smaller than the √350. This means that if we make use of the formula, √350 will give a lower confidence interval than that of √15. Therefore, the confidence interval would be narrower changing from a sample size of 15 to a sample size of 350.

c) Applying the formula, a standard deviation of 15 pounds would result to a lower confidence interval than a standard deviation of 20 pounds. Therefore, the confidence interval would be wider changing from a standard deviation of 15 pounds to a standard deviation of 20 pounds.

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The population of a certain country in 1996 was 286 million people. In​ addition, the population of the country was growing at a
Fudgin [204]

Answer:

A) In 2004 the population will reach 306 million.

B) In 2033 the population will reach 386 million.

Step-by-step explanation:

Given : The population of a certain country in 1996 was 286 million people. In​ addition, the population of the country was growing at a rate of 0.8​% per year. Assuming that this growth rate​ continues, the model P(t) = 286(1.008 )^{t-1996} represents the population P​ (in millions of​ people) in year t.

To find : According to this​ model, when will the population of the country reach A. 306 million? B. 386 million?

Solution :

The model represent the population is P(t) = 286(1.008 )^{t-1996}

Where, P represents the population in million.

t represents the time.

A) When population P=306 million.

306 = 286(1.008 )^{t-1996}

\frac{306}{286}=(1.008 )^{t-1996}

1.0699=(1.008 )^{t-1996}

Taking log both side,

\log(1.0699)=\log((1.008 )^{t-1996})

\log(1.0699)=(t-1996)\log(1.008)  

\frac{\log(1.0699)}{\log(1.008)}=(t-1996)  

8.479=t-1996  

t=8.479+1996

t=2004.47

t\approx2004

Therefore, In 2004 the population will reach 306 million.

B) When population P=386 million.

386 = 286(1.008 )^{t-1996}

\frac{386}{286}=(1.008 )^{t-1996}

1.3496=(1.008 )^{t-1996}

Taking log both side,

\log(1.3496)=\log((1.008 )^{t-1996})

\log(1.3496)=(t-1996)\log(1.008)  

\frac{\log(1.3496)}{\log(1.008)}=(t-1996)  

37.625=t-1996  

t=37.625+1996

t=2033.625

t\approx2033

Therefore, In 2033 the population will reach 386 million.

6 0
3 years ago
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