A manufacture of rayon wants to compare that the yield strength of 5 11⋅ kg/ 2 mm is
met or not at 5% level of significance. The manufacturer draws a sample and
calculates the mean to be 8 12⋅ kg/ 2 mm and the standard derivation is known to be
2⋅0kg/ mm .
2
Carry out the statistical test appropriate for this.
Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.
Based on the information provided, the significance level is and degrees of freedom.
The critical value for a two-tailed test is
The rejection region for this two-tailed test is
The - statistic is computed as follows:
Since it is observed that it is then concluded that the null hypothesis is rejected.
Therefore, there is enough evidence to claim that the population mean is different than at the significance level.
Using the P-value approach: The p-value for two-tailed, the significance level and degrees of freedom is
and since it is concluded that the null hypothesis is rejected.
Therefore, there is enough evidence to claim that the population mean is different than at the significance level.
Therefore, there is enough evidence to claim that the yield strength is different than at the significance level.
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