Simplify.
2 answers:
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Answer:
Step-by-step explanation:
Hello!
The researcher is interested in comparing how many hours per week the students dedicate to studying regarding their gender.
Let 1 denote the females and 2 denote the males, the parameter of interest will be the difference between the average weekly study hours of female students and the average weekly hours of study of male students, symbolically:
μ₁ - μ₂
If the objective is to see if there is any difference between the average weekly study hours, the statistical hypotheses are:
H₀: μ₁ - μ₂ = 0
H₁: μ₁ - μ₂ ≠ 0
α: 0.02
The calculated statistic is = 2.86
This Hypothesis test is two-tailed, meaning that the rejection region is divided in two tails, using the critical value approach:
The decision rule is:
If ≤ -2.334 or if
≥2.334, then you reject the null hypothesis.
If -2.334 < < 2.334, then you do not reject the null hypothesis.
is greater than the upper critical value, so the decision is to reject the null hypothesis.
Then using a 2% significance level, the test is significant, you can conclude that the population mean weekly study hours of female students and the population mean weekly hours of study of male students are different.
I hope this helps!
Using the binomial distribution, it is found that:
a) There is a 0.1618 = 16.18% probability that among 18 randomly observed individuals exactly 6 do not cover their mouth when sneezing.
b) There is a 0.104 = 10.4% probability that among 18 randomly observed individuals fewer than 3 do not cover their mouth when sneezing.
c) 9 is more than 2.5 standard deviations below the mean, hence it would not be surprising if fewer than half covered their mouth when sneezing.
<h3>What is the binomial distribution formula?</h3>The formula is:
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
The values of the parameters are given as follows:
n = 18, p = 0.267.
Item a:
The probability is P(X = 6), hence:
There is a 0.1618 = 16.18% probability that among 18 randomly observed individuals exactly 6 do not cover their mouth when sneezing.
Item b:
The probability is:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).
Then:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0037 + 0.0245 + 0.0758 = 0.104.
There is a 0.104 = 10.4% probability that among 18 randomly observed individuals fewer than 3 do not cover their mouth when sneezing.
item c:
We have to look at the mean and the standard deviation, given, respectively, by:
- E(X) = np = 18 x 0.267 = 4.81.
9 is more than 2.5 standard deviations below the mean, hence it would not be surprising if fewer than half covered their mouth when sneezing.
More can be learned about the binomial distribution at brainly.com/question/24863377
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