What is the value of the expression below?<br> -4(5

A survey in Men’s Health magazine reported that 39% of cardiologists said that they took vitamin E supplements. To see if this i

zzz [600]

Answer:

$z=\frac{0.36 -0.39}{\sqrt{\frac{0.39(1-0.39)}{100}}}=-0.615$

The p value for this case would be:

$p_v =2*P(z$

For this case since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not different from 0.39

Step-by-step explanation:

Information given

n=100 represent the random sample taken

X=36 represent the number of people that take E supplement

$\hat p=\frac{36}{100}=0.36$ estimated proportion of people who take R supplement

$p_o=0.39$ is the value that we want to test

$\alpha=0.05$ represent the significance level

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to test if the true proportion is equatl to 0.39 or not, the system of hypothesis are.:

Null hypothesis: $p=0.39$

Alternative hypothesis: $p \neq 0.39$

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing the info we got:

$z=\frac{0.36 -0.39}{\sqrt{\frac{0.39(1-0.39)}{100}}}=-0.615$

The p value for this case would be:

$p_v =2*P(z$

For this case since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not different from 0.39

8 0

3 years ago

The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years

inn [45]

Answer:

b. The null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0$

c. Student's t distribution, as it is a two-sample test for the difference between means.

d. Test statistic t = 5.42.

P-value = 0

e. They appear to be significantly different, as the sample data gives strong evidence that the difference is greater than 0.

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that the mean life spans in the county is significantly different for whites and nonwhites.

Then, the null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0$

The significance level is 0.05.

The sample 1 (white), of size n1=124 has a mean of 45.3 and a standard deviation of 12.7.

The sample 2 (non-white), of size n2=82 has a mean of 34.1 and a standard deviation of 15.6.

The difference between sample means is Md=11.2.

$M_d=M_1-M_2=45.3-34.1=11.2$

The estimated standard error of the difference between means is computed using the formula:

$s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{12.7^2}{124}+\dfrac{15.6^2}{82}}\\\\\\s_{M_d}=\sqrt{1.301+2.968}=\sqrt{4.269}=2.066$