# Q4 STAT Formative Assessment #5

## Quiz by JONALD ROSARIO

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- Q1
What is the formula for the confidence interval of the population mean when the population variance is known?

$\backslash overline\{\backslash mathrm\{x\}\}\backslash \; \backslash pm\backslash \; Z\backslash \; \backslash frac\{\backslash delta\}\{\backslash sqrt\{n\}\}$

$\backslash overline\{\backslash mathrm\{x\}\}\backslash \; \backslash pm\backslash \; t\backslash \; \backslash frac\{s\}\{\backslash sqrt\{n\}\}$

30s - Q2
What is the formula for the confidence interval of the population mean when the population variance is unknown?

$\backslash overline\{\backslash mathrm\{x\}\}\backslash \; \backslash pm\backslash \; t\backslash \; \backslash frac\{s\}\{\backslash sqrt\{n\}\}$

$\backslash overline\{\backslash mathrm\{x\}\}\backslash \; \backslash pm\backslash \; Z\backslash \; \backslash frac\{\backslash delta\}\{\backslash sqrt\{n\}\}$

30s - Q3
In constructing a confidence interval for the population mean, if the confidence level increases, what happens to the width of the confidence interval?

Increases

Stays the same

Decreases

Depends on the sample size

30s - Q4
A researcher wants to estimate the average height of students in a university with 95% confidence. If the population standard deviation is 4 inches and the sample size is 100, what is the margin of error?

0.78 inch

0.64 inch

0.96 inch

1.28 inch

30s - Q5
A random sample of 50 observations is drawn from a normally distributed population. The sample mean is 75 and the population standard deviation is 10. What is the 90% confidence interval for the population mean?

$75\backslash \; \backslash pm\backslash \; 1.96$

$75\backslash \; \backslash pm\backslash \; 1.645$

$75\backslash \; \backslash pm\backslash \; 1.96\backslash \; \backslash times\backslash \; \backslash frac\{10\}\{\backslash sqrt\{50\}\}$

$75\backslash \; \backslash pm\backslash \; 1.645\backslash \; \backslash times\backslash \; \backslash frac\{10\}\{\backslash sqrt\{50\}\}$

30s - Q6
In constructing a confidence interval for the population mean with unknown variance, which distribution is used to determine the critical value?

T-distribution

Chi-square distribution

Normal distribution

F-distribution

30s - Q7
A researcher wants to estimate the average weight of newborn babies in a hospital with 95% confidence. If a sample of 25 newborns has a sample mean weight of 7 pounds and a sample standard deviation of 1.5 pounds, what is the margin of error?

0.62 pounds

0.97 pounds

0.51 pounds

0.78 pounds

30s - Q8
A random sample of 27 observations is drawn from a population with an unknown variance. The sample mean is 50, and the sample standard deviation is 8. What is the 95% confidence interval for the population mean?

50±1.96×$\backslash frac\{8\}\{\backslash sqrt\{27\}\}$

50±2.056×$\backslash frac\{8\}\{\backslash sqrt\{27\}\}$

50 ± 2.056

50 ± 1.96

30s - Q9
A researcher wants to estimate the average time spent daily on social media by teenagers with 90% confidence. If a sample of 25 teenagers shows a mean time of 2.5 hours and a sample standard deviation of 0.5 hours, what is the margin of error?

0.312 hour

0.171 hour

0.156 hour

0.624 hour

30s - Q1030s