One method for straightening wire prior to coiling it to make a spring is called
ID: 3230959 • Letter: O
Question
One method for straightening wire prior to coiling it to make a spring is called "roller straightening". Suppose that a sample of 18 wires is selected and each is tested to determine tensile strength (N/mm^2). The resulting sample mean and sample standard deviation are 2174.4 and 31.5, respectively. It is known that the mean tensile strength for spring made using spinner straightening is 2152 N/mm^2. (1) What is the random variable X in this problem? What does the mean mu of X represent? (2) What null hypothesis and alternative hypothesis should be tested in order to determine if the mean tensile strength for the roller method is better than the mean tensile strength for spinner method? (3) Is this one-tailed or two-tailed test? (4) What test statistic should be used to test the hypotheses? Is a normality assumption of the population necessary? Why? (5) At the significance level alpha = 0.10, compute the rejection region (RR). (6) Compute the value of your test statistic (assuming H_0). (7) What is the conclusion of your test? Explain in your own words, avoiding statistical terms as possible.Explanation / Answer
Solution:-
1) The The mean tensile strngth of springs are avariable X in this problem. The mean of X represents that the mean of the mean tensile strength for spinner method is 2152 N/m2.
2)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: < 2152
Alternative hypothesis: > 2152
3) Note that these hypotheses constitute a one-tailed test.
4) Formulate an analysis plan. For this analysis, the significance level is 0.10. The test method is a one-sample t-test, because sample size is less than 30 and population standard deviation is not known.
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 = 7.425
DF = n - 1 = 18 - 1
D.F = 17
5) tcritical = 1.74
t = (x - ) / SE
6) t = 3.02
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.
The observed sample mean produced a t statistic test statistic of 3.02. We use the t Distribution Calculator to find P(t > 3.02) = 0.003859
Interpret results. Since ththe P-value (0.003859) is less than the significance level (0.10), we have to reject the null hypothesis.
From the above test we conclude that mean tensile strength for roller method is better than the mean tensile strngth for spinner method.
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