3(25%)The conversion of raw materials to products of a chemical process is being

Question

3(25%)The conversion of raw materials to products of a chemical process is being studied. From previous experience with this process the standard deviation of the conversion is known to be 2.8. The past 5 days of plant operation have resulted in the following conversions (given in percentages): 916, 88.75, 90.8, 89.95 and 91.3%. Use = 0.05. Perform hypothesis testing to check if the mean conversion is 90% or not? (a) (5%) write the null and alternative hypothesis: (b)(10%) Use the fixed-level test, check if there is sufficient evidence that the mean conversion is not 90%? Circle: YES or NO (c) (10%)Find a 99% two-sided CI on the true mean conversion. Round the answers to i decimal place. 1

Explanation / Answer

Part a

Null hypothesis: H0: The mean conversion is 90%.

Alternative hypothesis: Ha­: The mean conversion is not 90%.

H0: µ = 90% versus Ha: µ 90%

Part b

Here, we have to use one sample z test for population mean.

Test statistic = Z = (Xbar - µ)/[/sqrt(n)]

We are given

= 2.8

= 0.05

Lower critical value = -1.96

Upper critical value = 1.96

(using z-table)

From given data, we have

Xbar = 90.48

Z = (90.48 – 90)/[2.8/sqrt(5)]

Z = (90.48 – 90)/ 1.2522

Z = 0.3833

P-value = 0.7015

(By using z-table)

P-value > = 0.05

So, we do not reject the null hypothesis that The mean conversion is 90%.

There is NO sufficient evidence that the mean conversion is not 90%.

Answer: NO

Part c

Here, we have to find 99% confidence interval for population mean.

Confidence interval = Xbar -/+ Z*/sqrt(n)

Confidence level = 99%

Critical Z value = 2.5758 (By using z-table)

Confidence interval = 90.48 -/+ 2.5758*2.8/sqrt(5)

Confidence interval = 90.48 -/+ 3.2254

Lower limit = 90.48 – 3.2254 = 87.3

Upper limit = 90.48 + 3.2254 = 93.7

Confidence interval = (87.3, 93.7)

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