Summary statistics are given for independent simple random samples from two populations. Preliminary data analysesindicate that the variable under consideration is normally distributed on each population. Decide whether use of thepooled t-test and pooled t-interval procedure is reasonable. Explain your answer.
-$\bar { x } _ { 1 } = 143.9 , \mathrm {~s} _ { 1 } = 17.2 , \mathrm { n } _ { 1 } = 7 , \bar { x } _ { 2 } = 212.9 , \mathrm {~s} _ { 2 } = 47.7 , \mathrm { n } _ { 2 } = 17$
A)Reasonable; the sample standard deviations suggest that the two population standard deviations are equal.
B) Reasonable; the sample standard deviations suggest that the two population standard deviations differ, however since the sample sizes are roughly equal, it is reasonable to use the pooled t-test.
C) Not reasonable; the sample standard deviations suggest that the two population standard deviations are equal, however since the sample sizes are not roughly equal, it is not reasonable to use the pooled t-test.
D) Not reasonable; the sample standard deviations suggest that the two population standard deviations differ and the sample sizes are not roughly equal.

Question

Summary statistics are given for independent simple random samples from two populations. Preliminary data analysesindicate that the variable under consideration is normally distributed on each population. Decide whether use of thepooled t-test and pooled t-interval procedure is reasonable. Explain your answer.
-$\bar { x } _ { 1 } = 143.9 , \mathrm {~s} _ { 1 } = 17.2 , \mathrm { n } _ { 1 } = 7 , \bar { x } _ { 2 } = 212.9 , \mathrm {~s} _ { 2 } = 47.7 , \mathrm { n } _ { 2 } = 17$  
A)Reasonable; the sample standard deviations suggest that the two population standard deviations are equal.
B) Reasonable; the sample standard deviations suggest that the two population standard deviations differ, however since the sample sizes are roughly equal, it is reasonable to use the pooled t-test.
C) Not reasonable; the sample standard deviations suggest that the two population standard deviations are equal, however since the sample sizes are not roughly equal, it is not reasonable to use the pooled t-test.
D) Not reasonable; the sample standard deviations suggest that the two population standard deviations differ and the sample sizes are not roughly equal.

Quizplus · Accepted Answer

The pooled t-test assumes that the two populations have equal variances. The sample standard deviations (17.2 and 47.7) suggest that the population variances are not equal, and the sample sizes (7 and 17) are not roughly equal, making the use of the pooled t-test not reasonable.

Summary Statistics Are Given for Independent Simple Random Samples from Two