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Answer: We are 95% confident that the mean SPF level of sunscreen used by all Cal Poly students is between 29.0813 and 40.0187.
Step-by-step explanation:
Given : Significance level : ![\alpha: 1-0.95=0.05](https://tex.z-dn.net/?f=%5Calpha%3A%201-0.95%3D0.05)
Sample size : n= 52 , which is a large sample (n>30), so we use z-test.
By using z-value table,
Critical value: ![z_{\alpha/2}=1.96](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3D1.96)
Sample mean : ![\overline{x}= 34.55](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%3D%2034.55)
Standard deviation : ![\sigma= 20.12](https://tex.z-dn.net/?f=%5Csigma%3D%2020.12)
The confidence interval for population means is given by :-
![\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%5Cpm%20z_%7B%5Calpha%2F2%7D%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
i.e. ![34.55\pm(1.96)\dfrac{ 20.12}{\sqrt{52}}](https://tex.z-dn.net/?f=34.55%5Cpm%281.96%29%5Cdfrac%7B%2020.12%7D%7B%5Csqrt%7B52%7D%7D)
![=34.55\pm5.46867829455\\\\\approx34.55\pm5.4687\\\\=(34.55-5.4687, 34.55+5.4687)=(29.0813,\ 40.0187)](https://tex.z-dn.net/?f=%3D34.55%5Cpm5.46867829455%5C%5C%5C%5C%5Capprox34.55%5Cpm5.4687%5C%5C%5C%5C%3D%2834.55-5.4687%2C%2034.55%2B5.4687%29%3D%2829.0813%2C%5C%2040.0187%29)
Now, the 95% confidence interval for the ppopulation mean = . (29.0813, 40.0187)
Hence, We are 95% confident that the mean SPF level of sunscreen used by all Cal Poly students is between 29.0813 and 40.0187.
A. The cost of no bags of kettle corn. With no bags, there will be no cost.
Answer:
It mean's numeric form with exponents.
Step-by-step explanation:
Basically it's a way to write the number better without having to repeat it.
Answer:
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