Question

How do you solve these questions (i.e. can someone show their work please)? The answers are already shown here, but I do not how the solutions are arrived at. Thanks so much.

17. Eight marksmen, labeled A, B,...,H, shot at targets with two types of rifle. Their scores were as in the table below: Marksman LA B C D E F G H sample mean sample SD Rifle Type 1 93 99 90 87 85 94 88 91 90.875 4.45 Rifle Type 2 89 93 86 92 78 90 91 87 88.25 4.77 Difference Typel-Type2) 4 6 4 -5 7 4 -3 4 2.625 4.27 (1) To perform the hypothesis testing, is there any assumption needed? (a) No assumption is needed. (b) Differences are assumed to follow the t distribution. (c) Differences are assumed to follow the Normal distribution. (d) Differences are assumed to follow the Binomial distribution. (2) When testing the hypothesis that the rifles are of equal quality, what is the test statistic? (a) 1.1381 (b) 1.7388 (c) 2.4452 (d) 2.4590 (3) What is the P-value for this hypothesis test? (a) Greater than 0.2 (b) Between 0.1 and 0.2 (c) Between 0.05 and 0.1 (d) Between 0.02 and 0.05 (4) Is there a significant difference between the two types of rifles at the 10% significant level? (a) Yes. (b) No. (c) There is insufficient information to tell.

Answer 1

Answer Date: 08/08/2019 To test the hypothesis is that there is a significant difference between the two types of rifles at 10% significance level. The null and alternative hypothesis is, Hold = 0 H:Hq 0 The boxplot for difference in score between type 1 rifle and type 2 rifle is, By using MINITAB software, draw boxplot with the help of following steps: 1) Import the data. 2) Select the Stat and choose the Basic Statistics option. 3) Select the Paired t and choose variable option and put First sample and Second sample. 4) Select Boxplot of differences from Graphs option. 5) Click Ok.

Boxplot of Differences (with Ho and 95% t-confidence interval for the mean) -5.0 -2.5 0.0 2: 5 Differences 5 .0 7.5 From the MINITAB output, the boxplot for difference in score between type 1 rifle and type 2 rifle concludes the shape of differences is approximately normally distributed and there is no outlier present in the plot. The answer is c.

2) The t-test statistics is, Vsan 2.625 |(4.27)?/8 = 1.7388 The t-test statistics is 1.7388. The answer is b. The p-value for this test is, From the t distribution table, show the degree of freedom 7 (n-1) and t-test statistics is 1.7388 and the p-value is between 0.10 and 0.20.

The answer is 6. 4) Decision The conclusion is that the p-value in this context is higher than 0.10 which is between 0.10 and 0.20, so the null hypothesis is not rejected at 10% level of significance. There is insufficient evidence to indicate that is a significant difference between the two types of rifles. The result is not statistically significant. to in the morning and use it hele en The answer is b.