Question

A toy manufacturer claims that its bestselling toy, robotracer, can run continuously for an average of 3 hours on a single charge. a parents' group, skeptical of this claim, tests 25 robotracers and finds that they have a mean run-time of 2.8 hours with a standard deviation of 0.4 hours. using a significance level of α=0.05, what conclusion should the parents' group make based on a two-tailed t-test? assumptions: population mean ( μ): 3 hours sample mean ( xˉ): 2.8 hours sample size ( n): 25 sample standard deviation (s): 0.4 hours

Answer 1

The parents' group's test results do not provide sufficient evidence to reject the manufacturer's claim that robotracer can run continuously for an average of 3 hours on a single charge, based on a two-tailed t-test with a significance level of α=0.05 and assumptions of population mean (μ) = 3 hours, sample mean (xˉ) = 2.8 hours, sample size (n) = 25, and sample standard deviation (s) = 0.4 hours.

Step-by-step explanation:

To perform a two-tailed t-test to determine whether the parents' group's test results provide sufficient evidence to reject the manufacturer's claim, we can use the following steps:

1. Check the assumptions:

- Population mean (μ): The manufacturer claims that the mean run-time is 3 hours.

- Sample mean (xˉ): The parents' group found a mean run-time of 2.8 hours.

- Sample size (n): The parents' group tested 25 robotracers.

- Sample standard deviation (s): The parents' group found a standard deviation of 0.4 hours.

2. Calculate the test statistic:

- Degrees of freedom (df) = n - 1 = 24

- T-score = (xˉ - μ) / (s / sqrt(n)) = (-0.2) / (0.4 / sqrt(25)) = -1.6

3. Look up the critical value:

- Significance level (α) = 0.05

- Critical value (t* ) = ±1.711 for a two-tailed test with df=24 (from a t-distribution table or statistical software).

4. Compare the test statistic and critical value:

- Since the calculated t-score (-1.6) falls between the critical values (-1.711, 1.711), we cannot reject the null hypothesis at the α=0.05 level of significance. This means that there is not enough evidence to conclude that the manufacturer's claim is false, and we should continue to assume that the mean run-time is 3 hours.

5. Interpret the results:

- The parents' group's test results do not provide sufficient evidence to reject the manufacturer's claim that robotracer can run continuously for an average of 3 hours on a single charge, based on a two-tailed t-test with a significance level of α=0.05 and assumptions of population mean (μ) = 3 hours, sample mean (xˉ) = 2.8 hours, sample size (n) = 25, and sample standard deviation (s) = 0.4 hours.