Statistical Inference and Hypothesis Testing Review

These flashcards cover key terms and concepts related to statistical inference and hypothesis testing.

Null Hypothesis (H0)

A statement that there is no effect or no difference, and it serves as a starting point for statistical testing.

Alternative Hypothesis (Ha)

The statement that there is an effect or a difference, which we seek evidence to support.

P-value

The probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true.

Type I Error

Rejecting the null hypothesis when it is actually true.

Type II Error

Failing to reject the null hypothesis when it is actually false.

Confidence Interval

A range of values derived from a sample that is likely to contain the value of an unknown population parameter.

Margin of Error

The amount of error that can be tolerated in a statistical estimate, affecting the width of the confidence interval.

Sample Proportion (p̂)

The proportion of a sample that has a particular characteristic, used as an estimate of the population proportion.

Significance Level (α)

The probability of making a Type I error, typically set at 0.05.

Random Sampling

A method of selecting a sample in which every member of the population has an equal chance of being included.

Normal Distribution

A probability distribution that is symmetric about the mean, creating a bell-shaped curve.

Standard Deviation of the Sample Proportion

An estimate of the variability of the sample proportion, calculated as sqrt[(p(1-p))/n].

Power of a Test

The probability that a statistical test will correctly reject a false null hypothesis.

Binomial Distribution

A probability distribution that sums the probabilities of a fixed number of trials, each with two possible outcomes.

Critical Value

A boundary value that defines the region where the null hypothesis is rejected.

Sample Size (n)

The number of observations in a sample, which affects the precision and reliability of estimates.

Failure Rate (q)

The probability of failing to achieve the desired outcome in a binomial distribution, where q = 1 - p.

Statistical Significance

A determination that an observed effect is likely not due to chance alone, usually assessed through p-values.

Hypothesis Testing

A statistical method used to decide whether to accept or reject a null hypothesis based on sample data.

Two-Tailed Test

A hypothesis test that considers both directions of a potential effect or difference.

One-Tailed Test

A hypothesis test that considers only one direction of a potential effect or difference.

Z-test

A statistical test for the means of a sample when the population variance is known.

T-test

A statistical test used to compare the means of two groups when the population standard deviations are unknown.

Sampling Distribution

The probability distribution of a statistic (e.g., sample mean) based on a large number of samples.

Confidence Level

The percentage of times that a confidence interval will contain the true population parameter if repeated samples are taken.

Standard Error

The standard deviation of the sampling distribution, indicating how much the sample proportion varies from the true population proportion.

Statistical Inference

The process of using data from a sample to make estimates or test hypotheses about a population.

Sampling Frame

A list or database of the members of the population from which a sample is drawn.

It is known that 12% of college students join a sports club. A random sample of 170 students is selected. What is the probability at least 14% of these students will joint a sports club?

0.2266

0.7734

0.2119

0.7881

In a random sample of 850​ consumers, 385 reported that they bought a PlayStation 5 above MSRP. Which of the following is a​ 98% confidence interval for the true population proportion of consumers that were bought a PlayStation 5 above MSRP?

(0.4248, 0.4810)

(0.4089, 0.4969)

(0.4194, 0.4864)


(0.4131, 0.4927)

Many consumers pay careful attention to stated nutritional contents on packaged foods when making purchases. It is therefore important that the information on packages be accurate. The null hypothesis is that the stated calorie content on a Red Baron pizza is 540. A random sample of 20 Red Baron pizzas was selected and used to test this null hypothesis. Which of the following describes a Type II​ error for this situation?

We conclude that the calorie content of the Red Baron pizza is​ 540 when it actually is 540.

We conclude that the calorie content of the Red Baron pizza is not 540 when it actually is different from 540.

We conclude that the calorie content of the Red Baron pizza is 540 when it actually is different from 540.

We conclude that the calorie content of the Red Baron pizza is not​ 540 when it actually is 540.

A biologist studying environmental pollutants finds that 32% of a random sample of salmon has high levels of mercury in their blood. The 90% confidence interval is found to be (0.23, 0.41). A researcher has claimed that 45% of salmon has high levels of mercury. What can we conclude if we use the given confidence interval to test the claim?

Since 0.32 falls in the confidence interval, the researcher’s claim is incorrect.

Since 0.32 falls in the confidence interval, the researcher’s claim is correct.

Since 0.45 does not fall in the confidence interval, the researcher’s claim is incorrect.


Since 0.45 does not fall in the confidence interval, the researcher’s claim is correct.

A lab technician runs a test to check whether a piece of medical equipment is functioning properly (the null hypothesis is that the equipment is functioning properly). Which of the following describe a Type I error for this test?

A.The technician decides the equipment is functioning properly, but it is not.

B.The technician decides the equipment is functioning properly, and it is.

C.The technician decides the equipment is not functioning properly, but it is.

D.The technician decides the equipment is not functioning properly, and it is not.

A polling agency wants to determine the percentage of voters in favor of extending tax cuts. They wish to estimate the percent to within 2% with 95% confidence. How many individuals should be included in the sample

A. 9604

A business article has found that 18% of adults have renters insurance. Suppose we randomly select 120 adults and find that 15% of them have renters insurance. Which of the following correctly describes the distribution for the sample proportion of adults in our sample who have renters insurance?

ô ~ AN(0.18, 0.0351)

ô ~ AN(0.15, 0.0326)

X ~ B(120, 0.15)

p ~ AN(0.18,0.0326)

4. It is known that​ 35% of all students change their major in college. In a random sample of 500​ students, what is the probability that at most​ 36% of these students will change their​ major?

0.0176

0.6808

0.2000

0.3192

A hypothesis test was conducted to test whether less than​ 50% of recent college graduates had a job offer prior to graduation. Assuming the null hypothesis is that only​ 50% have a job​ offer, a test statistic of z​ = -2.30 was calculated. When testing at the​ 5% significance​ level, which is the most appropriate​ conclusion?

The conclusion cannot be determined from the information given.

There is sufficient evidence to conclude less than​ 50% of recent college graduates had a job offer prior to graduation.

There is not sufficient evidence to conclude less than​ 50% of recent college graduates had a job offer prior to graduation.

There is sufficient evidence to conclude that only​ 50% of recent college graduates had a job offer prior to graduation.

In testing the hypotheses H0: p= 0.82 vs Ha: p= 0.82? The test statistic is calculated to be 1.73. Which of the following would be the correct p-value?

0.9582

0.0418

0.0836

1.9164

Which of the following will increase the width of a confidence interval for the proportion? I. Increasing the confidence level
II. Increasing the sample size
III. Decreasing the confidence level
IV. Decreasing the sample size

I only

II only

II and III

III and IV

I and IV