Question

In 36 randomly selected hours of production, the mean and the standard deviation of the number of acceptable pieces produced by a automatic stamping machine are $\bar{x}=1,050$   and $s=130$

At the 0.05 level of significance, does this enable us to reject the null hypothesis μ= 1,000 against the alternative hypothesis μ≠ 1,000?

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Answer 1

Answer: consider, S. The bumber of acceptable pieces produe- ced by a automatic stamping machine. Xi sample means 1050 sample standard deviation = 130 no sample size = 36 jevel of significance *(Two sided) one sample t test is appropriate to use. stepli _Hypothesis, Hoi Il= 1000 Hiil 3 1000 = 0.05 ? Vs step 2: test statistic st = X-l astot SAB te 1050 - 1000 130/16 = 2.308

Step3: critical value =tola 2 t 36-1, 0.05 t35, 0.025 = 2.03 from t table. Step 4) Decision t statistic = 2.308 > t-crit= 2.03 we reject Ho Step 5) conclusion There is sufficient evidence the alternative bypothesis i's true الدب