Please answer a) b) and c) The sugar content of the syrup in canned peaches is n

Question

Please answer a) b) and c)

The sugar content of the syrup in canned peaches is normally distributed, and the variance is thought to be sigma^2 = 20 (mg)^2 (a) Test the hypothesis that the variance is not 20 (mg)^2 if a random sample of n = 12 cans yields a sample standard deviation of s = 5 mg, using a fixed-level test with alpha= 0.05. State any necessary assumptions about the underlying distribution of the data. (b) What is the P-value for this test? (c) Find a 95% two-sided CI for sigma. (d) Use the CI in part (c) to test the hypothesis. (e) Use MiniTab to obtain the results of a), b) and c)

Explanation / Answer

Part-a

We need to assume that the data from which the samle taken is normally distributed.

The results of two tail hypothesis test are as follows

Test and CI for One Variance

Method

Null hypothesis Sigma-squared = 20
Alternative hypothesis Sigma-squared not = 20

The chi-square method is only for the normal distribution.
The Bonett method cannot be calculated with summarized data.

Statistics

N StDev Variance
12 5.00 25.0

95% Confidence Intervals

CI for CI for
Method StDev Variance
Chi-Square (3.54, 8.49) (12.5, 72.1)

Tests

Test
Method Statistic DF P-Value
Chi-Square 13.75 11 0.494

Part-b

P-value of test=0.494

As p-value>0.05, we do not reject the null hypothesis and cocnlude that variance is 20 mg2

Part-c

95% cofnidence interval for sigma = (3.54, 8.49)

Part-d

As 95% confidence interval include sigma=sqrt(20)=4.47, so we do not reejc the null hypothesis

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