Please answer all questions. Lapsodiptia or Harnet\'s (HD) disease afflicts abou
ID: 3242706 • Letter: P
Question
Please answer all questions. Lapsodiptia or Harnet's (HD) disease afflicts about 50,000 people in the U.S. Recently it has been discovered that there are two types of Harnet's disease. At the Harnet's Disease Research Center in Harper's Ferry, WV, scientists are developing a test to distinguish the differences between Type I and Type II Harnet's disease. They want to measure different levels of diptoprotein in tissue surrounding the ears. These scientists feel that there is a difference in the mean levels of diptoprotein for the two types of HD. They sample tissue from 40 patients with Type I HD and 40 patients with Type II HD. For the former group they find that mean diptoprotein level was 78.46 with a standard deviation of 9.24. For the Type II group, the mean level of diptoprotein was 84.26 with a standard deviation of 8.90. Using alpha = 0.05, test the hypothesis of interest. The average (mean) length of workweeks (in hours) of 15 randomly selected employees in the mining industry and 10 randomly selected employees in the manufacturing industry were obtained. Assuming both distribution are Normal, test the hypothesis that the two industries have the same mean length of workweek using alpha = 0.10. The sample mean from the mining industry was 47.5 and the sample standard deviation was 5.5, the sample mean for the manufacturing industry was 43.5 and the sample standard deviation was 5.7. Designers of whooping crane casts need to estimate the average length of whooping crane legs. In particular they need to determine if male and female whooping cranes have legs of equal length. They use data from 32 male cranes and 32 female cranes collected by the Appalachia Club. For the sample of 32 females the sample mean length was 37.8 inches with sample standard deviation of 6.6 inches. For the sample of 32 males the sample mean length was 39.1 inches with sample standard deviation of 5.2 inches. Determine if there is a difference in mean leg length for male and female whooping cranes using alpha = 0.10.Explanation / Answer
Solution:-
3)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 = 2
Alternative hypothesis: 1 2
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.10. 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 = 1.485
DF = 62
t = [ (x1 - x2) - d ] / SE
t = - 0.875
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 62 degrees of freedom is more extreme than - 0.875; that is, less than - 0.875 or greater than 0.875.
Thus, the P-value = 0.385
Interpret results. Since the P-value (0.385) is greater than the significance level (0.10), we have to accept the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that there is difference in mean length for the mle and female whopping cranes.