A company has developed a new ink-jet cartridge for its printer. Hence, the comp
ID: 2926672 • Letter: A
Question
A company has developed a new ink-jet cartridge for its printer. Hence, the company needs to investigate whether new cartridge’s average lifetime changed from the one currently being produced. To investigate its length of life, 96 of the new cartridges were tested by counting the number of high-quality printed pages each was able to produce. The sample mean and standard deviation were determined to be 1510.099 pages and 35.124 pages, respectively. The historical mean lifetime for cartridges produced by the current process is 1513.751 pages. At alpha, = 0.1 do the following.
State Null and Alternative hypotheses.
Indicate the tail or side (Left, Right or Two-tail).
Find the critical value.
Calculate the test statistic.
Make a conclusion either reject or not rejecting the Null hypothesis. And interpret the results. In your own words, explain implication of Type I and Type II errors for this case.
What will happen if company commits Type I and Type II errors?
Explanation / Answer
Solution:-
State the hypotheses.The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: = 1513.751
Alternative hypothesis: 1513.751
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.10. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 3.585
DF = n - 1
D.F = 95
t = (x - ) / SE
t = - 1.02
tcritical = 1.661
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
Since we have a two-tailed test, the P-value is the probability that the t statistic having 95 degrees of freedom is less than -1.02 or greater than 1.02.
Thus, the P-value = 0.3104
Interpret results. Since the P-value (0.3104) is greater than the significance level (0.10), we cannot reject the null hypothesis.
In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis while a type II error is incorrectly retaining a false null hypothesis.
More simply stated, a type I error is the (false) detection of an effect that new cartridge’s average lifetime changed from the one currently being produced.
While a type II error is the failure to detect that new cartridge’s average lifetime changed from the one currently being produced, whwn actually change is present.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.