Complete questions 6,7,8.
1 answer:
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Answer:
Comparing the p value with the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that we have singificantly differences between the two proportions.
Step-by-step explanation:
Data given and notation
represent the number with no defects in sample 1
represent the number with no defects in sample 1
sample 1
sample 2
represent the proportion of number with no defects in sample 1
represent the proportion of number with no defects in sample 2
z would represent the statistic (variable of interest)
represent the value for the test (variable of interest)
significance level given
Concepts and formulas to use
We need to conduct a hypothesis in order to check if is there is a difference in the the two proportions, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We need to apply a z test to compare proportions, and the statistic is given by:
(1)
Where
z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
Calculate the statistic
Replacing in formula (1) the values obtained we got this:
Statistical decision
Since is a two sided test the p value would be:
Comparing the p value with the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that we have singificantly differences between the two proportions.
Using the binomial distribution, it is found that the probability that exactly 36 of them buy a product is of 0.044.
For each first-time visitor, there are only two possible outcomes, either they buy a product, or they do not. The probability of a first-time visitor buying a product is independent of any other first-time visitor, hence the binomial distribution is used to solve this question.
<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.
In this problem:
- 45% of first-time visitors to its website do not buy any of its products, hence 55% buy, that is, p = 0.55.
- There are 75 first-time visitors on a given day, hence n = 75.
The probability that exactly 36 of them buy a product is P(X = 36), hence:
More can be learned about the binomial distribution at brainly.com/question/24863377