Question

Battery life A tablet computer manufacturer claims that its batteries last an average of 10.5 hours when playing videos. The quality-control department randomly selects 20 tablets from each day’s production and tests the fully charged batteries by playing a video repeatedly until the battery dies. The quality control department will discard the batteries from that day’s production run if they find convincing evidence that the mean battery life is less than 10.5 hours. Here are a dot plot and summary statistics of the data from one day:

a. State appropriate hypotheses for the quality-control department to test. Be sure to define your parameter.

b. Check if the conditions for performing the test in part (a) are met.

Short answer

Part a)$$\begin{gathered} H_0:\mu =10.5 \\ {H}_a:\mu <10.5 \end{gathered}$$

Part b) Large sample condition is not satisfied.

Step-by-step solution

Part a) Step 1: Given information

The claim is that means is less than$10.5$

Part b) Step 2: The objective is to explain the state appropriate hypothesis for the quality-control department to test. 

The null hypothesis states that the population value is equal to the claim value: $H_0:\mu =10.5$

The null hypothesis or the alternative hypothesis is the claim. The null hypothesis asserts that the population means equals the value specified in the claim. If the claim is the null hypothesis, then the alternative hypothesis statement is the inverse of the null hypothesis.

$H_1:\mu <10.5$

localid="1654460033100" $\mu$is the mean battery lifetime.

Part b) Step 1: Given information

Given:

Part b) Step 2: The objective is to find the conditions for performing the test in part (a) are met

Random, independent (condition), and Normal/ Large sample are the three conditions.

Random: Satisfied because the tablets were chosen at random.

Independent: Satisfied, because the sample of 20 tablets represents less than $10\%$of the total tablet population.

Normal/large sample size: Dissatisfied because the sample size of 20 tablets is small and the distribution in the dot plot is skewed.

Because the Normal/Large sample condition is not met, a hypothesis test for the population mean is not appropriate.