Construct a 95% Confidence Interval for the ounces in the bottles.

Mean ounce is 15.370 ounces

The confidence interval is 95%

Margin of error is =SE/Sqrt (30)

CRITICAL VALUE=

Alpha (α): α = 1 – (confidence level / 100) = 1 – 0.95 = 0.05

Z critical values=0.05/2=0.025

CI=mean± (critical value) {SD/Sqrt N) =1.960 (0.555/5.477)

=0.1986±Mean

=15.5686 OR 15.1714

We can be 95% confident that the mean drying time is between 15.5686 or 15.1714 since the margin of error IS 0.025

Hypothesis;

HO: The bottles of the brand of soda produced in the company contain the advertised sixteen (16) ounces of product. Mean = 16

H1= The bottles of the brand of soda produced in the company contain less than the advertised sixteen (16) ounces of product Mean ≠ 16

Solution

Step 1: Set the null and alternative hypotheses

HO:. Mean = 16

H1= Mean ≠ 16

Step 2: Calculate the test statistic

15.370-16/(0.550/sqrt 30=-0.63/0.1004

=-6.274

Step 3: Set Rejection Region

R : /Z/ > 6.0

Step 4: Conclude

It is clear that /-6.274)= /-6.274>6.0. Therefore, the test statistics is in the rejection area. The conclusion is to reject the hull hypothesis in favors of the alternative hypothesis. It is therefore healthy to conclude that the mean is very different from 16 ounces, that the claims by the customer is right as the ounces is not 16 as advertised

Strategies

If you conclude that there are less than sixteen (16) ounces in a bottle of soda, speculate on three (3) possible causes. Next, suggest the strategies to avoid the deficit in the future.

The three main causes of the poor measurements include;

Wrong calibration- if the machines for measuring the ounces of products in the bottle is wrongly calibrated, it leads to wrong measurements

If the system is not standardized and the system is automated, the system may lead to production of varying ounces of the products (Morien, 2007)

Finally, there are errors in the filing process, where the products sampled are m not properly filled within the system and the people charged with filing the bottles are to blame for this (Wegner, 2010).

Strategies

In order to avoid the deficit in future, it is important to conduct an SPC (statistical process control) to determine the upper limit and the lower limit. This way, the management can set the lowest and the highest limit and any bottle not filed within the range is considered deficit. The process should also be calibrated and automated to control and maintain the measurement of the ounces in the bottles (Wise, & Fair, (1998).

Anderson-Darling

Data is Normal

A-Squared

0.630

p

0.091

95% Critical Value

0.787

99% Critical Value

1.092

Mean

15.370

Mode

15.300

Standard Deviation

0.550

Variance

0.303

Skewedness

0.642

Kurtosis

0.105

N

30.000

Minimum

14.500

1st Quartile

15.025

Median

15.300

3rd Quartile

15.575

Maximum

16.600

Confidence Interval

0.205

for Mean (Mu)

15.165

0.95

15.575

For Stdev (sigma)

0.438

0.740

for Median

15.100

15.400

References

Wise, Stephen A. & Fair, Douglas C (1998). Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. ASQ Quality Press

Morien, D. (2007) Business Statistics, Thomson Learning Nelson

Wegner, T. (2010). Applied Business Statistics: Methods and Excel-Based Applications, Juta Academic

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