Question

A certain type of battery supercharger was found to take a mean of 14.6 minutes to charge a standard electric vehicle (EV) battery. A firmware update for this type of supercharger was recently released, but the update has received negative reviews from users. A researcher suspects the mean time the updated superchargers take to charge a standard EV battery is greater than 14.6 minutes. To test his claim, he chooses 19 of the updated superchargers at random and measures the time it takes each one to charge a standard EV battery. He finds that the superchargers take a sample mean of 14.7 minutes to charge a standard EV battery, with a sample standard deviation of 3.4 minutes. Assume that the population of amounts of time to charge a standard EV battery using the updated superchargers is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.10 level of significance, to support the claim that μ, the mean time the updated superchargers take to charge a standard EV battery, is more than 14.6 minutes.

(a) State the null hypothesis H₀ and the alternative hypothesis H₁ that you would use for the test.
H₀ :
H₁ :
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Answer 1

To test if updated superchargers take longer to charge EV batteries, one must state the null hypothesis H₀: μ = 14.6 (mean charge time remains unchanged) and the alternative hypothesis H₁: μ > 14.6 (mean charge time increased). A t-test is applicable here due to the small sample size and unknown population standard deviation, with the level of significance set at 0.10.

Step-by-step explanation:

To perform a hypothesis test to determine if there is enough evidence at the 0.10 level of significance to support the claim that the mean time the updated superchargers take to charge a standard EV battery is more than 14.6 minutes, we begin by stating the null and alternative hypotheses.

Null Hypothesis (H₀)

The null hypothesis (H₀): μ = 14.6, which indicates that the mean charge time after the firmware update is equal to the mean charge time before the update.

Alternative Hypothesis (H₁)

The alternative hypothesis (H₁): μ > 14.6, which signifies that the mean charge time after the firmware update is greater than the mean charge time before the update.

With a sample mean of 14.7 minutes, a sample standard deviation of 3.4 minutes, and sample size of 19 superchargers, we would conduct a t-test since the population standard deviation is unknown and the sample size is less than 30. The level of significance (α) of the test is 0.10.