Hypothesis Testing for Population Mean by formula?

2016-04-22 1:22 pm

Suppose the director of a manufacturer of external battery for iPhone needs to determine whether its new production line is producing batteries in accordance with the company’s specification: the average capacity of batteries is 3000mA. A random sample of 45 batteries gives a mean of 2900mA and a standard deviation of 380mA.

a) Perform the hypothesis testing at 5percent level of significance (α).
i) State the null and alternative hypothesis.
ii) Determine the rejection region and draw a graph to represent it.
iii) Determine the test statistic and make the statistical decision.
b) Following the conclusion in a), determine whether the new production line is functioning properly.
c) Construct a 95percent confidence interval for the average capacity of batteries.
d) Use the interval in c) to perform the hypothesis in a). Compare the conclusion with the one in a).

I need the calculation steps , thank you very much!

回答 (1)

cidyah

2016-04-22 1:58 pm

✔ 最佳答案

i) Let μ be the average capacity of external batteries for iPhone

H0 : μ = 3000mA
Ha: μ ≠ 3000mA

ii)
Rejection region is t > 2.0154 or t < -2.0154
Indicate 2.0154 and -2.0154 in the graph

http://s1169.photobucket.com/user/chibuckt/media/one_an2_zpswpcprnpv.gif.html?filters[user]=127216769&filters[recent]=1&sort=1&o=0
iii)
Sample mean = 2900
Standard deviation = 380
Standard error of mean = s / √ n
Standard error of mean = 380 / √ 45
SE = 380/6.7082
Standard error of mean 56.6471
t = (xbar- μ ) / SE
t = (2900-3000) / 56.6471
t = -1.7653

Calculated t does not fall in the rejection region, so do not reject H0;

b)
New production line is producing batteries in accordance with the company’s specification:

c)
Standard error of mean = 380 / √ 45
SE = 380/6.7082
Standard error of mean 56.6471
95% confidence interval 2900-(56.6471)(2.0154) and 2900+(56.6471)(2.0154)

(2785.83, 3014.17)

d)
The confidence interval encloses 3000mA so don't reject H0.

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