hypothesis testing w/ z scores

a z score is the measure of

how many standard deviations a score is above or below the mean of its distribution

Suppose we have a population with a mean of 25 and a standard deviation of 7.

One value in that population is 21. What is the Z score for that value?

-0.57

What are the critical cutoff values for Z scores if I want to isolate the most extreme 2.5% of the normal distribution in each tail?

Z =± 1.96

A desperate statistician believes that using corny stats jokes as pick-up lines will increase the number of dates he goes on. Statisticians, as a group, typically go on 1.4 dates per year, σ = 0.6

After using corny pick-up lines for a year he went on 0 dates. What should the statistician conclude about the
value of stats jokes?

this data supports the idea that stat jokes have an effect on dates

A researcher knows that the average Atlantic puffin has an average top speed of 55 mph, with a standard deviation of 6mph. I am going to track 9 randomly selected puffins and measure their top speeds.

Based on the information above, what is the standard error?

2

A researcher believes that Chipotle's burritos make college students happier. Without burritos, college students' happiness is normally distributed with a mean of 5.9 with a standard deviation of 1.4

After giving 5 students Chipotle's burritos, she measures the students' average happiness at 8.0.
What Z score would be associated with this sample?

1.5