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Answer:
7.1+/-0.48
= (6.62, 7.58) hours
Therefore, the 95% confidence interval (a,b)= (6.62, 7.58) hours
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = 7.1 hours
Standard deviation r = 0.78 hour
Number of samples n = 10
Confidence interval = 95%
z value(at 95% confidence) = 1.96
Substituting the values we have;
7.1+/-1.96(0.78/√10)
7.1+/-1.96(0.246657657493)
7.1+/-0.483449008686
7.1+/-0.48
= (6.62, 7.58) hours
Therefore, the 95% confidence interval (a,b)= (6.62, 7.58) hours
The 95% confidence interval of the mean time is (6.62,7.58) and this can be determined by using the formula of the confidence interval.
Given :
- Ten randomly selected people were asked how long they slept at night.
- The mean time was 7.1 hours, and the standard deviation was 0.78 hour.
The following steps can be used in order to determine the 95% confidence interval of the mean time:
Step 1 - The formula of the confidence interval can be used in order to determine the 95% confidence interval of the mean time.
Step 2 - The formula of the confidence interval is given below:
[tex]\rm CI = \bar{x}\pm z_{\alpha /2}\times \dfrac{\sigma}{\sqrt{n} }[/tex]
where the standard deviation is [tex]\sigma[/tex] and the sample size is 'n'.
Step 3 - Now, substitute the values [tex]\rm \bar{x}[/tex], [tex]\sigma[/tex], n and z in the above expression.
[tex]\rm CI = 7.1\pm 1.96\times \dfrac{0.78}{\sqrt{10} }[/tex]
Step 4 - Simplify the above expression.
[tex]\rm CI = 7.1\pm0.48[/tex]
So, the 95% confidence interval of the mean time is (6.62,7.58).
For more information, refer to the link given below:
https://brainly.com/question/2396419
