Question

1. Determine why a hypothesis test should not be run on the following samples:

   1. A restaurant wants to show that its customer service rating is better than the ratings on Yelp. Currently they have 3.2 stars out of 5. A small set of survey cards are left at tables for customers to fill out and rate the service if they like. Results from 230 customers shows an average rating of 3.7 stars out of 5, with a standard deviation of 0.6 stars.

   2. Currently, a company sends out hundreds of thousands of cards asking for donations to the Red Cross, and only receives donations from 1.2% of those requests. They have developed a new letter with updated visuals and nicer fonts in hopes of increasing donation rates. Out of 200 test cards sent, 3% of them returned with a donation.

   3. A school with 300 students wants to show that the proportion of students that use its library at least once a week is higher than 30%. They take a sample of 60 students and find that 33% of them use the library at least once a week.

   4. A company wants to show that the mean salary for all of its employees, including managers, CEOs, etc., is higher than 28 thousand. They take a random sample of 10 employees and find that the mean salary is 32 thousand with a standard deviation of 4.8 thousand.

Answer 1

There are three assumptions for conducting analysis in hypothesis testing.
1. The dependent variable is assessed using a scale measure.
2. The participants are randomly selected.
3. The distribution of the population of interest must be approximately normal.

We are not using hypothesis testing because of following reason.

Example 1. Restaurant

Sample collected is not simple random sample.

We are not sure about distribution of population is approximately normal or not.

Example 2. Donation

Sample is not randomly collected

We are not sure distribution of population is approximately normal or not.

Example 3.

Population is skewed .

It does not follow approximately normal distribution.

Example 4.

Population is skewed