Hypothesis Testing for Population Mean by formula?
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
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!
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
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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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