A company that manufactures laptop batteries claims the mean battery life is 16 hours. Assuming the distribution of battery life
1 answer:
Answer:
The appropriate test statistic for the hypothesis test is
Step-by-step explanation:
The null hypothesis is:
The alternative hypothesis is:
The test statistic is:
In this equation, X signifies the sample mean, denotes the value under the null hypothesis, s is the standard deviation of the sample, and n represents the sample size.
In this scenario:
Thus
The correct test statistic for the hypothesis test is
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The 99% confidence interval for the actual mean difference between average mail-order and internet purchase amounts falls within [$(-31.82), $12.02].
Step-by-step clarification:
We know a random sample of 16 mail-order sales receipts shows a mean sale amount of $74.50 and a standard deviation of $17.25.For internet sales, a random sample of 9 receipts gives a mean sale amount of $84.40 with a standard deviation of $21.25.
The pivotal value utilized for constructing a 99% confidence interval for the true mean difference is given by;
P.Q. =~
where, = sample mean of mail-order sales = $74.50
= standard deviation for mail-order sales = $17.25
= standard deviation for internet sales = $21.25
= number of mail-order sales receipts = 16
= number of internet sales receipts = 9
= = 18.74
The actual mean difference between average mail-order and internet purchases is denoted by (
Thus, the 99% confidence interval for () is expressed as;
= Here, the t critical value at the 0.5% significance level with 23 degrees of freedom is 2.807. =
= [$-31.82, $12.02]
Complete Question
The complete question appears in the first uploaded image
Answer:
a) Yes, selecting 15 corresponds to a binomial experiment
b)
c)
d)
Regarding question a:
For an experiment to qualify as binomial
the trials have to be independent
each trial must yield one of two possible outcomes
Given that the selection of 15 individuals is random, we ascertain that the trials are independent and the outcomes are “either the individual saves for retirement or does not save for retirement.”
Therefore, we conclude that the selection of 15 people at random is indeed a binomial experiment.
In question b:
The probability that all selected adults do not save for retirement is mathematically modeled as
r = 15 implies all selected adults
n refers to the population size equating to 15
From the problem, p = 0.20
and q can be calculated as
=>
=>
Thus
Regarding question c:
The probability that exactly five of the selected adults do not save for retirement is mathematically modeled as
In relation to question d:
The probability that at least one of the selected adults opts not to save for retirement can be mathematically expressed as