A square has the sides length 2k-1 units. An equilateral triangle has the sides of the length k+2 units. the square and the tria
1 answer:
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Answer:
a) We would expect to see 500*0.88=440
b)
So the p value obtained was a very high value and using the significance level assumed we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion is not significant different from 0.9.
The p value is a criterion to decide if we reject or not the null hypothesis, when we reject the null hypothesis in other case we FAIL to reject the null hypothesis. And represent the "probability of obtaining the observed results of a test, assuming that the null hypothesis is correct".
Step-by-step explanation:
Data given and notation
n=500 represent the random sample taken
X=450 represent the people that have the seat belt fastened
estimated proportion of people that have the seat belt fastened
is the value that we want to test
represent the significance level
z would represent the statistic (variable of interest)
Alternative hypothesis:
When we conduct a proportion test we need to use the z statisitc, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level assumed is . The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
So the p value obtained was a very high value and using the significance level assumed we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion is not significant different from 0.9.
The p value is a criterion to decide if we reject or not the null hypothesis, when we reject the null hypothesis in other case we FAIL to reject the null hypothesis. And represent the "probability of obtaining the observed results of a test, assuming that the null hypothesis is correct".
Answer:
98% confidence interval for the average age of all students is [24.302 , 25.698]
Step-by-step explanation:
We are given that a random sample of 36 students at a community college showed an average age of 25 years.
Also, assuming that the ages of all students at the college are normally distributed with a standard deviation of 1.8 years.
So, the pivotal quantity for 98% confidence interval for the average age is given by;
P.Q. = ~ N(0,1)
where, = sample average age = 25 years
= population standard deviation = 1.8 years
n = sample of students = 36
= population average age
So, 98% confidence interval for the average age, is ;
P(-2.3263 < N(0,1) < 2.3263) = 0.98
P(-2.3263 < < 2.3263) = 0.98
P( <
<
) = 0.98
P( <
<
) = 0.98
98% confidence interval for = [
,
]
= [ ,
]
= [24.302 , 25.698]
Therefore, 98% confidence interval for the average age of all students at this college is [24.302 , 25.698].