Univaritive statistics Part 2

Question 1

What is a hypothesis in statistics?

Answer 1

An unproven proposition or statement made to explain phenomena, tested through statistical methods.

Question 2

What is the purpose of hypothesis testing?

Answer 2

To determine which of the two hypothesis (null or alternative) is more likely to be correct based on the sample data

Question 3

What is the significane level (a)?

Answer 3

The probability threshold (commonly 0.05) below which the null hypothesis is rejected

Question 4

When to reject the null hypothesis?

Answer 4

When p-value < 0.05 or the calculated test statistic is more extreme than the critical value

Question 5

When would you fail to reject the null hypothesis?

Answer 5

If the p-value is > 0.05 or the calculated test statistic is within the critical range

Question 6

What are Type I and Type II errors?

Answer 6

• Type I: rejecting a true null hypothesis
• Type II: Failing to reject a false null hypothesis

Question 7

What does the t-distribution represent?

Answer 7

• A symmetrical, bell shaped distribution used when sample sizes are small and population standard deviation is known

Question 8

What is a one sample t-test?

Answer 8

• A hypothesis test that uses the t-distribution to compare a sample mean against a known or hypothesised population mean

Question 9

What is the degrees of freedom in a t-test?

Answer 9

The number of observations minus the number of constrints; affects the shape of the t-distribution

Question 10

what does it mean if the calculated t-value > critical t value?

Answer 10

The result is statistically significant; reject the null hypothesis

Question 11

How is a confidence interval for a population mean calculated?

Answer 11

Using the sample mean, standard deviation, sample size, and crtical t-value from the t-distribtuion table

Question 12

What is the chi - square test for goodness of fitness?

Answer 12

A test to determine if the observed frequency distribution differs significantly from the expected distribution

Question 13

When is a chi - square test appropriate?

Answer 13

For analyzing categorical data like gende or brand preference

Question 14

What indicates a significant result in a chi-square test?

Answer 14

The calculated Xsquared value is greater than the critical Xsquared value at the chosen signifcance level