A shelf contains n separate compartments. There are r indistinguishable marbles.
1 answer:
Answer:
ways
Step-by-step explanation:
Given that a shelf contains n separate compartments. There are r indistinguishable marbles
The marbles are identical so they can be placed in any order.
Let us consider the places available for placing these r marbles
No of compartments available =n
Marbles to be placed = r
Since marbles are identical and order does not matter
number of ways the r marbles can be placed in the n compartments
= nCr
=
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Answer:
a)
The null hypothesis is:
The alternative hypothesis is:
b) For men is of 0.49 and for women is of 0.36.
c) The p-value of the test is 0.0039 < 0.01, which means that the results are statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year.
Step-by-step explanation:
Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Men:
98 out of 200, so:
Women:
72 out of 200, so:
a. State the hypothesis test in terms of the population proportion of men and the population proportion of women.
At the null hypothesis, we test if the proportion are similar, that is, if the subtraction of the proportions is 0, so:
At the alternative hypothesis, we test if the proportion of men is greater, that is, the subtraction is greater than 0, so:
b. What is the sample proportion for men? For women?
For men is of 0.49 and for women is of 0.36.
c. Use α= 0.01 level of significance. What is the p-value and what is your conclusion?
From the sample, we have that:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis, and s is the standard error, so:
P-value of the test and decision:
The p-value of the test is the probability of finding a difference above 0.13, which is the p-value of z = 2.66.
Looking at the z-table, z = 2.66 has a p-value of 0.9961.
1 - 0.9961 = 0.0039.
The p-value of the test is 0.0039 < 0.01, which means that the results are statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year.
Answer:
The probability is
Step-by-step explanation:
From the question we are given that
The population mean is
The standard deviation is
The random number
The sample size is
The probability that the sample mean would be greater than
Generally the z- score of this normal distribution is mathematically represented as
Now
substituting values
Which implies that
Now from the z-table the probability is found to be