Answer:
120in.
Step-by-step explanation:
The pic attached
Triangle ABC is a right triangle and cos(22.6o)=StartFraction b Over 13 EndFraction. Solve for b and round to the nearest whole
2 answers:
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Answer:
So on this case the 95% confidence interval would be given by (11.393;15.857)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Data: 14, 10, 13, 16, 12, 18, 15, 11
We can calculate the sample mean and deviation with the following formulas:
represent the sample mean
population mean (variable of interest)
s=2.669 represent the sample standard deviation
n=8 represent the sample size
Calculate the confidence interval
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,7)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (11.393;15.857)
Answer:
<em>a)95% confidence intervals for the population mean of light bulbs in this batch</em>
(325.5 ,374.5)
b)
<em>The calculated value Z = 4 > 1.96 at 0.05 level of significance</em>
<em>Null hypothesis is rejected </em>
<em>The manufacturer has not right to take the average life of the light bulbs is 400 hours.</em>
Step-by-step explanation:
Given sample size n = 64
Given mean of the sample x⁻ = 350
Standard deviation of the Population σ = 100 hours
The tabulated value Z₀.₉₅ = 1.96
<em>95% confidence intervals for the population mean of light bulbs in this batch</em>
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(325.5 ,374.5)
b)
<u><em>Explanation</em></u>:-
Given mean of the Population μ = 400
Given sample size n = 64
Given mean of the sample x⁻ = 350
Standard deviation of the Population σ = 100 hours
<u><em>Null hypothesis</em></u> : H₀:The manufacturer has right to take the average life of the light bulbs is 400 hours.
μ = 400
<u><em>Alternative Hypothesis: H₁:</em></u> μ ≠400
<u><em>The test statistic </em></u>
|Z| = |-4|
The tabulated value Z₀.₉₅ = 1.96
The calculated value Z = 4 > 1.96 at 0.05 level of significance
Null hypothesis is rejected.
<u><em>Conclusion:</em></u>-
The manufacturer has not right to take the average life of the light bulbs is 400 hours.