Q: A random sample of 200 Canadian households found that 40% owned dogs. If the population proportion is 34%, what is the z-score for this sample proportion?

$$z = \frac{0.40 - 0.34}{\sqrt{\frac{0.34 \times 0.66}{200}}} = 1.79$$

Q: What is the formula for the chi-square statistic used in a goodness-of-fit test?

$$\$$chi^2$$_{obs} = \sum \frac{(\text{Observed} - \text{Expected})^2$}{\text{Expected}}$$

Question 1

Which of the following statements about probability distributions is TRUE?

Accepted Answer

All probabilities in a probability distribution must sum up to unity (1).

Question 2

A researcher records the number of contacts stored on each student’s phone. What type of random variable is this?

Accepted Answer

Discrete random variable

Question 3

Given a normal distribution with mean $$\mu = 650$$ grams and standard deviation $$\sigma = 20$$ grams, what is the z-score for a newborn grizzly bear cub weighing 625 grams?

Accepted Answer

$$z = \frac{625 - 650}{20} = -1.25$$

Question 4

Which condition is NOT required for using the binomial distribution?

Accepted Answer

The probability of success must change from trial to trial.

Question 5

For a binomial experiment with $$n = 4$$ and $$p = 0.3$$, what is the probability of getting exactly 2 successes?

Accepted Answer

$$P(x=2) = 0.265$$

Question 6

Which formula gives the standard deviation of the sampling distribution of the sample proportion $$\hat{p}$$?

Accepted Answer

$$SD = \sqrt{\frac{p(1-p)}{n}}$$

Question 7

A random sample of 200 Canadian households found that 40% owned dogs. If the population proportion is 34%, what is the z-score for this sample proportion?

Accepted Answer

$$z = \frac{0.40 - 0.34}{\sqrt{\frac{0.34 	imes 0.66}{200}}} = 1.79$$

Question 8

In hypothesis testing, what is a Type I error?

Accepted Answer

Rejecting the null hypothesis when it is true.

Question 9

A 90% confidence interval for the true proportion of adults with tattoos in Kanturi is calculated as $$0.35 \pm 0.0278. $$What is the lower limit of this interval?

Accepted Answer

$$0.3222$$

Question 10

What sample size is required to achieve a margin of error of $$0.035$$ for an 85% confidence interval, given $$z^* = 1.44$$?

Accepted Answer

$$n = \frac{1}{4} \left( \frac{1.44}{0.035} \$$right)^2$$ \approx 424$$

Question 11

A population has a variance of 1000. What is the variance of the mean age for a random sample of 40 species?

Accepted Answer

$$\frac{1000}{40} = 25$$

Question 12

Which of the following is a condition for using the sample mean $$\bar{x} to $$estimate the population mean $$\mu$$?

Accepted Answer

The sample must be collected randomly and independently.

Question 13

Which hypothesis test is appropriate for comparing the means of three or more groups?

Accepted Answer

ANOVA (Analysis of Variance)

Question 14

What is the formula for the chi-square statistic used in a goodness-of-fit test?

Accepted Answer

$$\$$chi^2$$_{obs} = \sum \frac{(	ext{Observed} - 	ext{Expected})^2$}{	ext{Expected}}$$

Question 15

Which of the following is NOT a condition for conducting a chi-square test?

Accepted Answer

Data must be continuous measurements.

Question 16

In a controlled experiment, what is the main purpose of random assignment?

Accepted Answer

To ensure that treatment groups are as similar as possible except for the treatment.

Question 17

What is the main difference between a controlled experiment and an observational study?

Accepted Answer

Controlled experiments use random assignment to treatment groups, while observational studies do not.

Question 18

Which technique is used to reduce bias and increase statistical power by grouping similar subjects before random assignment?

Accepted Answer

Blocking

Question 19

Statistical power is the probability of:

Accepted Answer

Correctly rejecting the null hypothesis when it is false.

Statistics Review: Probability Distributions, Binomial & Normal Distributions, Proportions, Hypothesis Testing, and Chi-Square Tests

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