Question

Hypothesis Testing - Expressions in Context

Expressing ourselves in the context of the problem can be challenging. Especially since there isn't ONE exact way to write our sentences. There is a structure or format to it, but each individual will make that expression in their own words. Let's practice together with the following problem. After you post, review your peers' expressions to see the variety that is possible. Look for the key features but appreciate the diversity of expression.

Our Problem:

A seatbelt has been tested and found to protect 80% of passenger dummies from severe injury in a large crash testing study. Now researchers want to see if a seat belt constructed from new material will work even better.

1) What would be the null and alternative hypotheses for this hypothesis test? Express them both in symbols and in words in the context of this problem.

2) The new seat belt is tested and the P-value is found to be 0.367 with a significance level of 5% (or 0.05). What would you conclude about the new seat belt? Be sure to (1) state your decision regarding the null hypothesis and (2) what this means in the context of the problem.

Answer 1

here claim is seat belt constructed from new material will work even better

let us consider p is population proportion of passenger protect dummies from severe injury in a large crash testing study.

A seatbelt has been tested and found to protect 80% of passenger dummies from severe injury in a large crash testing study. Now researchers want to see if a seat belt constructed from new material will work even better.

1) the null and alternative hypotheses for this hypothesis test in words is

Ho:population proportion of passenger protect dummies from severe injury in a large crash testing study is 80%

Ho:population proportion of passenger protect dummies from severe injury in a large crash testing study is more than 80%

In symbols

Ho : p= 0.80

Ha: p >0.80

2) the P-value = 0.367 , since p value is greater rhan 0.05 so we dont reject Ho and conclude that population proportion of passenger protect dummies from severe injury in a large crash testing study is 80% which means that seat belt constructed from new material will not work better.