Find the value of x in the polygon
2 answers:
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Answer:
Since we can't assume that the distribution of X is the normal then we need to apply the central limit theorem in order to approximate the with a normal distribution. And we need to check if n>30 since we need a sample size large as possible to assume this.
Based on this rule we can conclude:
a. n = 14 b. n = 19 c. n = 45 d. n = 55 e. n = 110 f. n = 440
Only for c. n = 45 d. n = 55 e. n = 110 f. n = 440 we can ensure that we can apply the normal approximation for the sample mean
for n=14 or n =19 since the sample size is <30 we don't have enough evidence to conclude that the sample mean is normally distributed
Step-by-step explanation:
For this case we know that for a random variable X we have the following parameters given:
Since we can't assume that the distribution of X is the normal then we need to apply the central limit theorem in order to approximate the with a normal distribution. And we need to check if n>30 since we need a sample size large as possible to assume this.
Based on this rule we can conclude:
a. n = 14 b. n = 19 c. n = 45 d. n = 55 e. n = 110 f. n = 440
Only for c. n = 45 d. n = 55 e. n = 110 f. n = 440 we can ensure that we can apply the normal approximation for the sample mean
for n=14 or n =19 since the sample size is <30 we don't have enough evidence to conclude that the sample mean is normally distributed
Answer:
So with the p value obtained and using the significance level given we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 1% of significance the mean for the control group it's not significantly higher than the mean of the treatment group by 1 point.
Step-by-step explanation:
When we have two independent samples from two normal distributions with equal variances we are assuming that
And the statistic is given by this formula:
Where z follows a normal standard distribution
The system of hypothesis on this case are:
Null hypothesis:
Alternative hypothesis:
Or equivalently:
Null hypothesis:
Alternative hypothesis:
Our notation on this case :
represent the sample size for group control
represent the sample size for group treatment
represent the sample mean for the group control
represent the sample mean for the group treatment
And now we can calculate the statistic:
And now we can calculate the p value using the alternative hypothesis:
So with the p value obtained and using the significance level given we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 1% of significance the mean for the control group it's not significantly higher than the mean of the treatment group by 1 point.