a-1. In case the equal population variance is assumed, the test statistic would be , and for the given values, we have or .
The degree of freedom is 2n-2 or 12.
a-2. The test would be a left tailed-test. The p-value would be , for x being the standard t-distribution with 12 df. As can be seen, the p-value is greater than 0.10.
a-3. As the p-value is higher than 0.01 alpha level, we fail to reject the null, and conclude that or . Hence, the correct option would be
a-4. The correct option would be
The reason being that we fail to reject the null which is or . The conclusion that population mean 1 is indeed less than population mean 2 would happen when the null hypothesis is rejected.
b-1. The test statistic assuming that population variances are unknown would be , which would yield the same as before considering n1=n2. We have or .
b-2. The p-value would be the same as before, ie , which is greater than 0.10.
b-3. As before, the p-value is higher than 0.01 alpha level, we fail to reject the null, and conclude that or . Hence, the correct option would be
b-4. The correct option would be
The result and reasons remains same as before, since the test statistic and conclusion doesn't change. We again fail to reject the null, which is .
Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (You...
Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (You may find it useful to reference the appropriate table: z table or t table) H0: μ1 − μ2 ≥ 0HA: μ1 − μ2 < 0 x¯1x¯1= 249x−2x−2= 262s1 = 35s2 = 23n1 = 10n2 = 10a-1. Calculate the value of the test statistic under the assumption that the population variances are equal. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) a-2. Find the p-value. multiple choice 1p-value < 0.010.01 ≤ p-value...
Consider the following competing hypotheses and accompanying sample data (You may find it useful to reference the appropriate table: z table or t table) Ho: Pi - P22 MA: P1 - P2 @ X1 - 238 nu - 425 X2 - 263 n2 - 425 a. Calculate the value of the test statistic (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic...
Consider the following competing hypotheses and accompanying sample data. (You may find it useful to reference the appropriate table: z table or t table) H0: p1 − p2 ≥ 0 HA: p1 − p2 < 0 x1 = 250 x2 = 275 n1 = 400 n2 = 400 a. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal...
Consider the following hypotheses: He: μ28e The population is normally distributed. A sample produces the following observations: 56 67 62 81 8366 Conduct the test at the 1% level of significance. (You may find lt useful to reference the appropriate table: table or Цеье o. Calculate the value of the test statistic. (Negative value should be Indicated by a minus sign. Round Intermedlate caleulatlons to at least 4 declmal places and final answer to 2 declmal places.) Test statistic b....
Consider the following hypotheses: Hot 208 RAM 208 A sample of 74 observations results in a sample mean of 202. The population standard deviation is known to be 26. (You may find it useful to reference the appropriate table: z table or table) a-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic a-2. Find...
A random sample of five observations from three normally distributed populations produced the following data: (You may find it useful to reference the F table.) Treatments A C 20 1 9 25 25 22 27 21 24 24 26 2.1 22 23 19 XR - 23 SR6.5 S 4.5 S 4.5 Click here for the Excel Data File f. At the 5% significance level, what is the conclusion to the test? Reject Ho since the p-value is less than significance...
Consider the following hypotheses: H0: μ ≥ 160 HA: μ < 160 The population is normally distributed. A sample produces the following observations: 152 138 151 144 151 142 Conduct the test at the 1% level of significance. (You may find it useful to reference the appropriate table: z table or t table) a. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and...
Consider the following hypotheses: HO: > 220 HA: U <220 A sample of 72 observations results in a sample mean of 209. The population standard deviation is known to be 18. (You may find it useful to reference the appropriate table: z table or t table) a-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test...
Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (Note: the automated question following this one will ask you confidence interval questions for this same data, so jot down your work.) H0: μ1 − μ2 = 0 HA: μ1 − μ2 ≠ 0 x−1x−1 = 60 x−2x−2 = 56 σ1 = 1.62 σ2 = 10.20 n1 = 25 n2 = 25 Calculate the value of the test statistic. (Negative values should be indicated by...
Consider the following hypotheses: Họ: H = 174 HA: u < 174 A sample of 79 observations results in a sample mean of 171. The population standard deviation is known to be 25. (You may find it useful to reference the appropriate table: z table or t table) a-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal...