Hi everyone! Read through the material below, watch the videos, work on the Excel lecture and follow up with your instructor if you have questions.

Learning Outcomes.

• Determine if the data supports a hypothesis at a given significance level using known distributions.

Topic. This lesson covers: Inference about a Population Mean with Unknown Standard Deviation

• Openstax Introductory Statistics:
• Introductory Statistics by Sheldon Ross, 3rd edition: Section 9.4
• Statistics with Microsoft Excel by Beverly J. Dretzke, 5th ed., TDIST(x,df,tails), TINV(p,df), P. 140 – 153

WeBWorK. Sets 9.3-9.6

#### The Applied View

Watch the video Small Sample Inference for One Mean.

1. Why won’t the z-procedure work in most cases, particularly if the sample size is small?
2. Who invented t-inference procedures?
3. Compare a normal density curve with a t-distribution for a sample size of 3. How are the two distributions similar and how do they differ?
4. For a t-distribution, how are the degrees of freedom related to sample size?
5. For a 95% confidence interval, which is larger, z* or t*?

#### Exit Ticket

A used car dealer says that the mean price of a 2008 Honda CR-V is at least \$20,500. You suspect this claim is incorrect and find that a random sample of 14 similar vehicles has a mean price of \$19,850 and a standard deviation of \$1084. Is there enough evidence to reject the dealer’s claim at alpha = 0.05? Assume the population is normally distributed.