Question

question 13
5 pts
a sample of 15 students studied an average of 11 hours per week for a class, with a sample standard deviation of 4. using a 95% confidence, the null hypothesis is that they studied less than 10 hours per week.
what is the standard error? round to 3 decimal places.
1.033
1.030
1.035
1.040
question 14
5 pts
a sample of 15 students studied an average of 11 hours per week for a class, with a sample standard deviation of 4. using a 95% confidence, the null hypothesis is that they studied less than 10 hours per week.
what is the calculated t - test value?
0.970
0.960
0.968
0.956

Explanation:

Step1: Recall standard - error formula

The formula for the standard error (SE) of the mean is $SE=\frac{s}{\sqrt{n}}$, where $s$ is the sample standard deviation and $n$ is the sample size.

Step2: Identify values

We are given that $s = 4$ and $n=15$.

Step3: Calculate standard error

$SE=\frac{4}{\sqrt{15}}\approx\frac{4}{3.873}\approx1.033$

Step4: Recall t - test formula

The formula for the one - sample t - test statistic is $t=\frac{\bar{x}-\mu}{SE}$, where $\bar{x}$ is the sample mean, $\mu$ is the hypothesized population mean, and $SE$ is the standard error.

Step5: Identify values for t - test

We have $\bar{x}=11$, $\mu = 10$, and from the previous calculation $SE\approx1.033$.

Step6: Calculate t - test value

$t=\frac{11 - 10}{1.033}=\frac{1}{1.033}\approx0.968$

Answer:

Question 13: 1.033
Question 14: 0.968