Suppose that a research and development scientist is studying the burn times in the current model and the new model of road flare that his company produces. He hopes to show that the average burn time of the new flare is higher than that of the current flare. First, he collects a random sample of 60 flares of the current model and records the burn time for each one. Next, he collects a random sample of 50 flares of the new model and records the burn time for each one.

The first sample is single?peaked and slightly skewed left, and the second is roughly symmetric and bimodal. Neither sample has outliers. Some of the summary statistics for his two samples are displayed below.

Population Population
description Sample
size Sample
mean Sample standard
deviation
1 current model n1=60 x??1=15.83 s1=1.93
2 new model n2=50 x??2=16.67 s2=2.28

Select the statement that accurately assesses whether or not a two?sample t?test is valid in this experiment.

a. A two?sample t?test is not valid because it is not known whether the data come from normal populations.

b. A two?sample t?test is valid because the samples are independent, random, contain no outliers, and are large enough.

c. A two?sample t?test is not valid because the difference in the two sample standard deviations is more than 0.3.

d. A two?sample t?test is valid because the two samples are independent, random, and the burn times for the two types of flare are continuous, quantitative variables.

e. A two?sample t?test is not valid because the first sample has 60 observations, but the second sample has50 observations.

f. A two?sample t?test is not valid because the distribution of one sample is single?peaked but the other is not.