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Hypothesis Testing in Statistics Flashcards

Hypothesis Testing in Statistics Flashcards
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Type II error

You conclude that the null hypothesis is true, but it is false.

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Type I error

You conclude that the null hypothesis is false, but it is actually true.

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As the significance levels increase _____.

the width of the confidence interval decreases (the null hypothesis is more likely to be rejected)

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T-distribution

Distribution to use when we don't know the standard deviation of the population mean and we have a small sample

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Hypothesis Testing Conditions

The population size is at least 20 times larger than the sample.

The sampling method must be random.

There are only two outcomes for each sample.

There are at least 10 successes and 10 failures.

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A sample of 300 US cyclists shows 150 are happy with the rules. Find p_hat (an estimate of the proportion of rule-happy US cyclists).

p_hat = 150 / 300 = 0.5

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Hypothesis test decision criteria for the p-value

The null hypothesis is rejected if the p-value is less than or equal to the desired significance.

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Hypothesis Testing

The procedure used in statistics to see whether a particular hypothesis is acceptable.

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16 cards in set

Flashcard Content Overview

Hypothesis testing is an important part of statistical analysis and scientific research. In these flashcards we will review the following concepts:

  • Null hypothesis
  • Alternative hypothesis
  • Using the p-value for testing a mean
  • Calculating the z-score for comparisons of proportions
  • The conditions for hypothesis testing of a proportion
  • Testing of matched pairs
  • The relationship between confidence intervals and hypothesis testing
  • Type I and type II errors
Front
Back
Hypothesis Testing

The procedure used in statistics to see whether a particular hypothesis is acceptable.

Hypothesis test decision criteria for the p-value

The null hypothesis is rejected if the p-value is less than or equal to the desired significance.

A sample of 300 US cyclists shows 150 are happy with the rules. Find p_hat (an estimate of the proportion of rule-happy US cyclists).

p_hat = 150 / 300 = 0.5

Hypothesis Testing Conditions

The population size is at least 20 times larger than the sample.

The sampling method must be random.

There are only two outcomes for each sample.

There are at least 10 successes and 10 failures.

T-distribution

Distribution to use when we don't know the standard deviation of the population mean and we have a small sample

As the significance levels increase _____.

the width of the confidence interval decreases (the null hypothesis is more likely to be rejected)

Type I error

You conclude that the null hypothesis is false, but it is actually true.

Type II error

You conclude that the null hypothesis is true, but it is false.

P-value less than the significance level

Reject the null hypothesis

If your data plots as a linear normal probability with no outliers, which paired test is reasonable?

Paired t-test

For what value of alpha should you reject the null hypothesis when the P-value is 0.06?

alpha = 0.10

A paired sample from census data is used to determine if the average salary of Boston residents and California residents is different. What variable should be used?

Salary

A paired sample from census data is used to determine if the average salary of Boston residents and California residents is different. State the alternative hypothesis.

The average salary of Boston residents is not equal to that of California residents.

Methods to determine acceptance or rejection of null hypothesis

p-value and region of acceptance

Requirements to use the z test for a difference between two proportions

The samples must be independent.

n_1*p_1, n1*q_1, n_2*p_2 and n_2*q_2 must all be greater than or equal to 5.

If your data analysis shows a difference in two sample groups at a level of P < 0.20, can you conclude this difference exists in the entire population at the 10% confidence level?

No, there is not enough evidence that the difference exists.

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