A fellow classmate tosses 5 coins and finds that 3 of them come up tails. Which of the following is the best conclusion for her
2 answers:
<h2>Answer:</h2>
Option: A is the correct answer.
A.This could easily happen with a fair coin after only 5 flips.
<h2>Step-by-step explanation:</h2>As we know that when a coin is tossed 5 times than the total number of outcomes that are resulting from these flips are:
where:
Hence, the total outcomes that are possible are: 32
Also, when a coin is fair any of the possibility could come up:
- All are tails
- All are heads.
- One tail four heads.
- One head four tail.
- Two tail three heads.
- Two heads three tails.
Hence, option: A is the correct answer.
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Answer:
a)
The null hypothesis is
The alternative hypothesis is
b-1) The value of the test statistic is t = 1.86.
b-2) The p-value is of 0.0348.
Step-by-step explanation:
Question a:
Test if the battery life is more than twice of 5 hours:
Twice of 5 hours = 5*2 = 10 hours.
At the null hypothesis, we test if the battery life is of 10 hours or less, than is:
At the alternative hypothesis, we test if the battery life is of more than 10 hours, that is:
b-1. Calculate the value of the test statistic.
The test statistic is:
We have the standard deviation for the sample, so the t-distribution is used to solve this question
In which X is the sample mean, is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
10 is tested at the null hypothesis:
This means that
In order to test the claim, a researcher samples 45 units of the new phone and finds that the sample battery life averages 10.5 hours with a sample standard deviation of 1.8 hours.
This means that
Then
The value of the test statistic is t = 1.86.
b-2. Find the p-value.
Testing if the mean is more than a value, so a right-tailed test.
Sample of 45, so 45 - 1 = 44 degrees of freedom.
Test statistic t = 1.86.
Using a t-distribution calculator, the p-value is of 0.0348.