Consider the following to answer the question(s) below:
A consumer group was interested in comparing the operating time of cordless toothbrushes manufactured by two different companies. They took a random sample of 18 toothbrushes from Company A and 15 from Company B. Each was charged overnight and the number of hours of use before needing to be recharged was recorded. Company A toothbrushes operated for an average of 119.7 hours with a standard deviation of 1.74 hours; Company B toothbrushes operated for an average of 120.6 hours with a standard deviation of 1.72 hours. Do these samples indicate that Company B toothbrushes operate more hours on average than Company A toothbrushes?
-At α = 0.05,
A) we reject the null hypothesis.
B) we fail to reject the alternative hypothesis.
C) we can conclude that there is significant difference between the mean operating times of cordless toothbrushes manufactured by the two companies.
D) we fail to reject the null hypothesis. There is not enough evidence to indicate that Company B cordless toothbrushes operate longer, on average, than those of Company A.
E) we fail to reject the alternative hypothesis. There is strong evidence indicating that Company B cordless toothbrushes operate longer on average than those of Company A.

Question

Consider the following to answer the question(s) below:
A consumer group was interested in comparing the operating time of cordless toothbrushes manufactured by two different companies. They took a random sample of 18 toothbrushes from Company A and 15 from Company B. Each was charged overnight and the number of hours of use before needing to be recharged was recorded. Company A toothbrushes operated for an average of 119.7 hours with a standard deviation of 1.74 hours; Company B toothbrushes operated for an average of 120.6 hours with a standard deviation of 1.72 hours. Do these samples indicate that Company B toothbrushes operate more hours on average than Company A toothbrushes? 
-At α = 0.05,
A) we reject the null hypothesis. 
B) we fail to reject the alternative hypothesis. 
C) we can conclude that there is significant difference between the mean operating times of cordless toothbrushes manufactured by the two companies. 
D) we fail to reject the null hypothesis. There is not enough evidence to indicate that Company B cordless toothbrushes operate longer, on average, than those of Company A. 
E) we fail to reject the alternative hypothesis. There is strong evidence indicating that Company B cordless toothbrushes operate longer on average than those of Company A.

Quizplus · Accepted Answer

We need to conduct a two-sample t-test with the null hypothesis being that there is no difference in the mean operating times between the two companies (μA = μB) and the alternative hypothesis being that Company B toothbrushes operate more hours on average (μB > μA). Using a two-sample t-test with unequal variances and a significance level of α = 0.05, we get a t-value of 1.07 and a p-value of 0.145. Since the p-value is greater than α, we fail to reject the null hypothesis. Therefore, there is not enough evidence to indicate that Company B cordless toothbrushes operate longer, on average, than those of Company A.

Consider the Following to Answer the Question(s) Below