brightness standards. The average lumens (light produced) per bulb should be 160
ID: 3241904 • Letter: B
Question
brightness standards. The average lumens (light produced) per bulb should be 1600. Light Bright Illuminations tested 20 new bulbs with a mean of 1590 lumens and standard deviation of 100 lumens. Does the new line of bulbs meet industry brightness standards? Assume the amount of lumens per bulb is normally distributed and a confidence level of 95%. a. Indicate your null and alternative hypothesis b. Perform an appropriate test. c. Construct a 95% confidence interval to address the question. The Jump Co. is a leading producer of high performance and recreational trampolines. The R&D; department is looking to produce a new line of high performance trampolines. Two fabrics are being tested for tensile strength. The product designer would like to use fabric A, since previous reports have suggested its tensile strength is greater, on average, and a more durable fabric. The sampling statistics from the fabric tests are provided in Table 1. Should the company use Fabric A for their new line of trampolines (alpha = 0.05)? (show all work for full credit) In the last decade the development of artificial intelligence (AI) has progressed significantly. A typical test of AI is to compare the computer's ability to complete a task against a human's abilityExplanation / Answer
Solution:-
5. The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1< 2
Alternative hypothesis: 1 > 2 (claim, Fabric A has tensile strength greater than Fabric B)
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = sqrt[(52/55) + (32/32)] = 0.857785
DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }
DF = (52/55 + 32/32)2 / { [ (52 / 55)2 / (54) ] + [ (32 / 32)2 / (31) ] }
DF = 0.54139495093/ (0.00382614018 + 0.0025516633) = 84.887
t = [ (x1 - x2) - d ] / SE = [ (216 - 202) - 0 ] / 0.857785 = 16.32
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 84.88 degrees of freedom
We use the t Distribution Calculator to find P(t < 16.32)
The P-Value is < .00001.
The result is significant at p < .05
Interpret results. Since the P-value is less than the significance level, we cannot accept the null hypothesis.
Conclusion. Reject the null hypothesis. The tensile strength of Fabric A is greater than Fabric B, that Fabric A is prefferable.
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