Please answer typed not pics. 1.On the basis of extensive tests, the yield point
ID: 3226144 • Letter: P
Question
Please answer typed not pics.
1.On the basis of extensive tests, the yield point of a particular type of mild steel-reinforcing bar is known to be normally distributed with historical standard deviation 100. A sample of 35 bars was taken and has a sample mean of 8439 lbs. Suppose that the specifications are that the yield point of a particular type of mild steel-reinforcing bar should be 8475 lbs.
(a) In performing one-sample hypothesis tests, would we use z ? or t ? in this situation? Briefly explain why you would use one instead of the other.
(b) Is there sufficient evidence that the mean yield point is less than the specifications call for (the specs say 8475)? Conduct a hypothesis test, using the pvalue approach.
(c) State the kind of error could have been made in context of the problem.
(d) Now do part b again in R.
2.A dealer in recycled paper places empty trailers at various sites. The trailers are gradually filled by individuals who bring in old newspapers and magazines, and are picked up on several schedules. One such schedule involves pickup every second week. This schedule is desirable if the average amount of recycled paper is more than 1600 cubic feet per 2-week period. The dealer’s records for eighteen 2-week periods show the following volumes (in cubic feet) at a particular site: recycle=c(1660,1820,1590,1440,1730,1680,1750,1720,1900,1570,1700,1900,1800,1770,2010,1580,1620,1690) The mean and standard deviation are as follows: X¯ = 1718.3 and s = 137.8
(a) In performing one-sample hypothesis tests, would we use z ? or t ? in this situation? Briefly explain why you would use one instead of the other.
(b) Is there sufficient evidence that the mean amount of recycled paper is more than 1600 cubic feet per 2 week period? Conduct a hypothesis test.
(c) State the kind of error could have been made in context of the problem.
(d) Now do part b again in R
Explanation / Answer
Solution:-
(a) In performing one-sample hypothesis tests, would we use z, population standrad deviation is known, population is normally distributed and sample is larger than 30.
b)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: > 8475
Alternative hypothesis: < 8475
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample z-test.
Analyze sample data. Using sample data, we compute the standard error (SE), and the z statistic test statistic (z).
SE = s / sqrt(n)
S.E = 16.9
z = (x - ) / SE
z = - 2.13
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 z statistic test statistic of - 2.13. We use the z Distribution Calculator to find P(z < - 2.13) = 0.0166
Interpret results. Since the P-value (0.0166) is less than the significance level (0.05), we have to reject the null hypothesis.
From the aboce test we have sufficient evidence that mean yield point is less than the specifications call.
c) Type I error.
In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis.