Question

A consumer group was interested in comparing the operating time of cordless toothbrushes manufactured by two different companies. Group members 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 117.7 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?

a. Write the null and alternative hypotheses to test this claim. (2 pts.)

b. After performing a two sample t-test for the difference of two means, at t-test score of -4.77 was found. What would be the associated P-value? (1 pt.)

c. State your conclusion and explain in context using alpha = 0.05. (2 Pts.)

Answer 1

Answer a)

The null and alternative hypotheses to test this claim are as follows:

Ho: μ_A​ ≥ μ_B​

Ha: μ_A​ < μ_B​

Answer b)

Degrees of freedom = n_A + n_B - 2 = 15+18-2 = 31

P-value corresponding to t = -4.77 and df = 31 is 0.0000 [Obtained using p-value calculator. Screenshot below]

Answer c)

Since p-value = 0.0000 < 0.05, we reject the null hypothesis

At 0.05 significance level, there is enough evidence to claim that Company B toothbrushes operate more hours on average than Company A toothbrushes.