Tell us a question you need help A machine makes ball bearin

Tell us a question you need help

A machine makes ball bearings for use in other industrial machinery. The mean diameter of a particular type of ball bearing is 20 millimeters. Based on a new vendor for their raw materials, the Quality Assurance manager is worried that the current production runs will be outside of specification. To test this, 100 ball bearings (n = 100) were sampled. The mean of the sample is 21.3 millimeters and the SAMPLE standard deviation is 1.22 millimeters. Decide if the sample data supports the claim that the mean diameter is 20 millimeters. Use a 0.02 level of significance.

a. State the null and alternative hypotheses.

b. State the decision rule.

c. Based on the sample data, state your decision in terms of the null hypothesis (reject or not reject). You may use either method, comparing the test statistic to the critical value, or the p-value approach.

with

Solution

Given data is

Mean21.3000

SD1.2200

SEM0.1220

N100

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H0: x bar =20

Ha: x bar not equals 20

Two sided test.

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P value and statistical significance:
  The two-tailed P value is less than 0.0001
  By conventional criteria, this difference is considered to be extremely statistically significant.

Confidence interval:
The hypothetical mean is 20.0000
The actual mean is 21.3000
The difference between these two values is 1.3000
The   95% confidence interval of this difference:
From 1.0579 to 1.5421

Actual difference 1.30 lies within this interval

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This difference is significant.

H0 is rejected using p value.