Inferential Statistics

• Point Estimation
• Interval Estimation
• Hypothesis Testing

• Point Estimation
• Interval Estimation
• Hypothesis Testing

• Point Estimation
• Interval Estimation
• Hypothesis Testing

• Both $\hat{X}$ and $\mu$ are random varaibles.
• Only $\hat{X}$ is a random variable.
• Both are constant values.
• Only $\mu$ is random varaible.

The study found the following:

• $818$ of the females in the sample exercise on a regular basis.
• $924$ of the males in the sample exercise on a regular basis.
• The average time that the $1742$ students who exercise on a regular basis ($818 + 924$) spend exercising per week is$4.2$ hours.

1. What is the point estimate for the proportion of all female college students who exercise on a regular basis?
2. What is the point estimate for the proportion of all college students who exercise on a regular basis?
3. Which of the following has a point estimate of $4.2$?
   • The mean time that all college students who exercise on a regular basis spend exercising per week
   • The mean time that all college students spend exercising per week
   • The percentage of all college students who exercise on a regular basis

Which of the following is true regarding x̄, the average number of hours that the 150 sampled students exercise per week?

• It is an unbiased estimate for $µ$.
• It is not an unbiased estimate for $µ$ and probably underestimates $µ$.
• It is not an unbiased estimate for $µ$ and probably overestimates $µ$.

• A random sample of $10,000$ U.S. families with children from the state of Utah
• A random sample of $500$ U.S. families with children
• A random sample of $5,000$ U.S. families with children
• A random sample of $1,000$ U.S. families

1. Variable varies normaly and sample size is small($n < 30$)
2. Variable varies normaly and sample size is large
3. Variable does not vary normal and sample size is small
4. Variable does not vary normal and sample size is large

1. Based on the poll's results, estimate p, the proportion of all U.S. adults who believe the use of marijuana should be legalized, with a 95% confidence interval.
2. Give an interpretation of the margin of error in context.
3. Do the results of this poll give evidence that the majority of U.S. adults believe that the use of marijuana should be legalized?

1. Given a random newborn puppy, its weight has a $95$ chance of being between $0.9$ and $1.1$ pounds.
2. If we examine another $100$ newborn puppies, their mean has a $95$ chance of being in that interval.
3. We're $95\\%$ confident that this interval captured the true mean weight.

1. Calculate your puppy’s z-score (standard score).
   1. How much does your newborn puppy have to weigh to be in the top 10% in terms of weight?
   2. Suppose the weight of newborn puppies followed a skewed distribution. Would it still make sense to calculate z-scores?

1. How do you assess the statistical significance of a pattern whether it is a meaningful pattern or just by chance?
2. What’s the distribution of p-values?
3. Recently, a lot of scientists started a war against statistical significance. What do we need to keep in mind when using p-value and statistical significance?

1. What happens to a regression model if two of their supposedly independent variables are strongly correlated?
2. How do we test for independence between two categorical variables?
3. How do we test for independence between two continuous variables?

1. What’s the probability that this happens by chance?
2. How to avoid this kind of accidental pattern?