The 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]
<h3>
How to find the confidence interval for population mean from large samples (sample size > 30)?</h3>
Suppose that we have:
- Sample size n > 30
- Sample mean =
- Sample standard deviation = s
- Population standard deviation =
- Level of significance =
Then the confidence interval is obtained as
- Case 1: Population standard deviation is known
- Case 2: Population standard deviation is unknown.
For this case, we're given that:
- Sample size n = 90 > 30
- Sample mean = = 138
- Sample standard deviation = s = 34
- Level of significance = = 100% - confidence = 100% - 90% = 10% = 0.1 (converted percent to decimal).
At this level of significance, the critical value of Z is: 
= ±1.645
Thus, we get:
![CI = \overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}\\CI = 138 \pm 1.645\times \dfrac{34}{\sqrt{90}}\\\\CI \approx 138 \pm 5.896\\CI \approx [138 - 5.896, 138 + 5.896]\\CI \approx [132.104, 143.896] \approx [130.10, 143.90]](https://tex.z-dn.net/?f=CI%20%3D%20%5Coverline%7Bx%7D%20%5Cpm%20Z_%7B%5Calpha%20%2F2%7D%5Cdfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%5C%5CCI%20%3D%20138%20%5Cpm%201.645%5Ctimes%20%5Cdfrac%7B34%7D%7B%5Csqrt%7B90%7D%7D%5C%5C%5C%5CCI%20%5Capprox%20138%20%5Cpm%205.896%5C%5CCI%20%5Capprox%20%5B138%20-%205.896%2C%20138%20%2B%205.896%5D%5C%5CCI%20%5Capprox%20%5B132.104%2C%20143.896%5D%20%5Capprox%20%5B130.10%2C%20143.90%5D)
Thus, the 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]
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Answer:
I need help with this! PLEASE!!! SOMEONE HELP ME!
1.A space shuttle's wings are useless as it travels around the exosphere. Explain, in your own words, why the wings are so useless and how the shuttles can move around.
2.Explain, in your own words, the thermosphere and the stratosphere are our hottest atmosphere layers.
3.Explain, in your own words, how and why “shooting stars” occur. For example, why and what causes meteors to burn up.
4.Explain, in your own words, the importance of our ozone layer in the stratosphere.
5.Explain, in your own words, why weather only occurs in the troposphere.
please use your own words!
Step-by-step explanation:
a. -42 + (-17)
Note that one negative and one positive = negative
-42 + (-17) = -42 - 17 = -59
b. (-42)/(-7)
Note that when dividing or multiplying two negatives, the answer will be positive
(-42)/(-7) = 6
c. (-5)² = (-5)(-5) = 25
25 is your answer
hope this helps
Answer:
<h3>
you need to be more clear</h3>
Step-by-step explanation:
i am confused
Answer:
$3.78
Step-by-step explanation:
find 107%(100%=$54+7%=107%)
54*107/100= $57.78
find the amount of sale tax
57.78-54=$3.78
