Fifteen 7th graders were asked how many hours they spend doing homework each week and how many hours they spend watching televis
ion each week. the results are shown in the dot plots below
1 answer:
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Answer:
Organizations can use one-sample hypothesis test to determine if there are performance issues in many ways.
It can be applied to the performance of a sector, a machine, a product, an advertising campaing, etc.
For example, we can take the example of a machine. It may be claimed that a specific machine performs significantly worse than the average.
This average would be the population mean: the average performance of the machines of the same type or process.
Then, a sample of the performance of the machine in study is taken and the hypothesis test can be performed to test the claim that this machine performs significantly worse.
Step-by-step explanation:
For example, we have an historic performance for this type of machine of 100 units a day. The machine A in study is sampled 14 days and have a performance of 92 units a day, with a sample standard deviation of 12 units/day. We have to test the claim that the machine A makes less units per day than the average.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample has a size n=14.
The sample mean is M=92.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=12.
The estimated standard error of the mean is computed using the formula:
Then, we can calculate the t-statistic as:
The degrees of freedom for this sample size are:
This test is a left-tailed test, with 13 degrees of freedom and t=-2.4944, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.0134) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that machine A produces significantly less units per day than the average.