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Answer:
The null hypothesis was rejected.
Conclusion: The proportions of orders completed on the day of receiving is more than 95%.
Step-by-step explanation:
The hypothesis can be defined as:
<em>H₀</em>: The proportions of orders completed on the day of receiving is not more than 95%, i.e. <em>p</em> ≤ 0.95.
<em>Hₐ</em>: The proportions of orders completed on the day of receiving is more than 95%, i.e. <em>p</em> > 0.95.
The significance level of the test is <em>α</em> = 0.025.
The sample size is, <em>n</em> = 500.
As the sample size is large, the sampling distribution of sample proportion can be approximated by the Normal distribution.
The mean and standard deviation of this distribution are:
The test statistic is:
The sample proportion is:
Compute the test statistic as follows:
The decision rule is:
If the <em>p</em>-value is less than the significance level <em>α</em> then the null hypothesis is rejected.
Compute the <em>p</em>-value as follows:
*Use a <em>z</em>-table.
The <em>p</em>-value = 0.0202 < <em>α</em> = 0.025.
The null hypothesis will be rejected.
<u>Conclusion</u>:
As the null hypothesis was rejected at 2.5% level of significance, it can be concluded that the proportions of orders completed on the day of receiving is more than 95%.