X-13<-5 solve the inequality and graph the solution

The difference between teenage female and male depression rates estimated from two samples is 0.07. The estimated standard error

KATRIN_1 [288]

Answer:

The 95% confidence interval is $0.0112 < \mu_m - \mu_f < 0.1288$

Step-by-step explanation:

From the question we are told that

The sample mean difference is $\= x_m - \= x_f = 0.07$

The standard error is SE = 0.03

Given that the confidence interval is 95% then the level of significance is mathematically evaluated as

$\alpha = 100 - 95$

$\alpha = 5\%$

$\alpha =0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table, the value is $Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{ \alpha }{2} } * SE$

substituting values

$E = 1.96 * 0.03$

$E = 0.0588$

The 95% confidence interval is mathematically represented as

$(\= x_m - \= x_f ) - E < \mu_m - \mu_f$

substituting values

$0.07 - 0.0588 < \mu_m - \mu_f$

$0.0112 < \mu_m - \mu_f < 0.1288$

3 0

3 years ago

A study was conducted to determine how bacteria cells multiply over time in a controlled environment. In the study, the bacteria

DENIUS [597]

Answer:

Dependent variable → bacteria cell increase or population

Independent variable → time variable

Step-by-step explanation:

An independent variable has direct effect on the dependent variable. The independent variable can stand on it own and it is not change by the other variable you are trying to measure. The independent variable have direct effect on the dependent variable.

A dependent variable is actually the variable being tested in an experiment. The dependent variable is actually dependent on the independent variable.

The dependent variable in this scenario is the bacteria cell increase or the bacteria cell multiplication. The bacteria cell increase is dependent on the time . The time variable is the independent variable as it can stand on it own .

Dependent variable → bacteria cell increase or population

Independent variable → time variable

8 0

3 years ago

A group of high school athletes has an average GPA of 2.7 with a standard deviation of 0.9. a)Find the percentage of athletes wh

mart [117]

Answer:

a) The percentage of athletes whose GPA more than 1.665 is 87.49%.

b) John's GPA is 3.645.

Step-by-step explanation:

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 2.7, \sigma = 0.9$