Question

Match each scenario below with the most appropriate inferential technique. Group of answer choices

We want to test if at least half of students at a university feel as if the dorms need to be renovated.

We want to estimate the average number of calories in a combo meal at fast food restaurants.

The population standard deviation is unknown.

We want to test if the average number of miles that motorists drive between oil changes is greater than the recommended 3000 miles while assuming a population standard deviation of 1000 miles.

We want to test if high school marching bands are equally made up of freshmen, sophomores, juniors, and seniors.

We want to test if the average starting salary of software engineers out of college is greater than \$70,000. The population standard deviation is unknown. We want to estimate the proportion of people who speak more than one language fluently.

Answer 1

1) To test if atleast half of the students at the University feel as if the dorms need to be renovated, the most inferential technique will be z test for single proportion. Let the proportion of the students who feel dorm need to be renovated be P. Hypothesis can be framed as-

Null hypothesis : P 0.50

Alternative hypothesis : P < 0.50

And can be tested at given level of significance.

2) For estimating the average number of calories in a combo meal at fast food restaurant, sample mean calories can be calculated and t test for single mean can be applied (as standard deviation is unknown)

3) To test if the average number of miles that motorist drive between oil changes is greater than 3000 miles, z test for single mean can be used. (As standard deviation is known to be 1000 miles)

4) To test if the high school marching band are equally made up of juniors, freshmen, sophomores, and seniors, chi square test can be used.

The hypothesis can be framed as -

Null hypothesis: Number of students of each category in school marching band are equal.

Alternative hypothesis : Number of students of each category in school marching band are unequal.

Under null hypothesis, expected frequency in each category = 1/4 * Total number of students in the band.

This can be compared with the observed frequency of students in each category.

And accordingly chi square statistic can be calculated and test can be conducted.

5) To test the average starting salary of software engineer out of college is greater than $70,000, the t-test for single mean can be used (As standard deviation is unknown).

6) To estimate the proportion of people who speaks more than one language fluently, sample proportion can be calculated. This can be tested using the z test for single proportion.