Question

1. jada and han are working together on a science experiment. they want to determine whether rechargeable batteries are heavier when they are fully charged than when they are depleted. they collect 12 rechargeable batteries of the same type and connect 6 of them to phones until the charge in each battery runs down. the other 6 batteries are left fully charged. they record the weight of the batteries in each group and find that the difference in mean weights for the groups is 0.19 grams.

a. jada writes a computer program to recombine all the data into all 924 possible different groupings and finds that 208 of the different groupings have a difference in means of at least 0.19. find the proportion of groups that have a difference in means at least 0.19. is there enough evidence for jada to conclude that the difference in means is due to the batteries having lost charge? explain or show your reasoning.

Explanation:

Step1: Calculate the proportion

The proportion of groupings with a difference in means of at least 0.19 is found by dividing the number of groupings with the desired difference by the total number of groupings. The formula is $p=\frac{n}{N}$, where $n$ is the number of groupings with a difference in means of at least 0.19 and $N$ is the total number of groupings.
$p = \frac{208}{924}\approx0.225$

Step2: Analyze for significance

A common significance - level in hypothesis - testing is 0.05. If the proportion of groupings with a difference in means of at least 0.19 is high (in this case, 0.225), it means that the observed difference in means (0.19 grams) could easily occur by chance. So, there is not enough evidence to conclude that the difference in means is due to the batteries having lost charge.

Answer:

The proportion of groups that have a difference in means at least 0.19 is approximately 0.225. There is not enough evidence to conclude that the difference in means is due to the batteries having lost charge because this proportion is relatively high, indicating that the observed difference in means could occur by chance.