Question

There is one of each of the following tests described in the scenarios: one sample z test, one sample t test and a matched pair t test. For each scenario decide what type of hypothesis testing procedure is appropriate and explain why.

Scenario 1. A sunglass company wants potential customers to compare two types of lenses, the current lenses and lenses made with a new high-tech material. A random sample of 42 customers are asked to wear each type of lens for several days in the sun. After wearing each of the lenses, customers are asked to score the lenses on a scale of 1 to 10, with higher scores being best. To reduce bias the company randomizes the order in which each customer wears the different lenses. Each customer scores both sets of lenses. The customer’s scores are compared to see if the average difference in ratings are other than zero. What type of testing procedure is appropriate to test if the mean difference is other than zero?

Scenario 2. Natasha would like to know whether she has budgeted enough money on average per month for groceries while she is in college. She takes a random sample of 70 college students and asks them how much they spend a month on groceries per month. She calculates a mean of $212 and a standard deviation $30. Natasha has budgeted $200. Which test can she use to test whether she has budgeted enough for groceries per month?

Scenario 3. A manufacturer of seat belts routinely samples the strength of seat belts to ensure their product meets specifications. Past experience has indicated the breaking strength of seat belts is normally distributed with a standard deviation of ? = 4 ???. A random sample of 16 specimens yields an average breaking strength of 2003 psi. What type of procedure is appropriate to test whether the mean is other than the desired 2000 psi?

Answer 1

sol 1) A sunglass company wants potential customers to compare two types of lenses, the current lenses and lenses made with a new high-tech material

A random sample of 42 customers are asked to wear each type of lens for several days in the sun. After wearing each of the lenses, customers are asked to score the lenses on a scale of 1 to 10, with higher scores being best.

claim : if the average difference in ratings are other than zero.

the appropriate test we will use matched paired t test

because we use the same sample for testing to compare two types of lenses on the bases of customer rating for current lenses and after using new high tech material lenses.

sol2) Natasha would like to know whether she has budgeted enough money on average per month for groceries while she is in college

claim: she has budgeted enough for groceries per month

we use t test for one sample because in this case she takes random sample

n= 70

sample mean = $212

sample standard deviation = $70

hypothesised mean = $200

so in this case population standard deviation are unknown so we use t test for one sample .

3)  A manufacturer of seat belts routinely samples the strength of seat belts to ensure their product meets specifications.

population standard deviation = 4psi

random sample = 16

sample mean =2003psi

hypothesised mean =2000psi

so we use one sample z test because we know the population standard deviation