Assignment 3 Total Marks: 50

Open Date: November 3, 2021, Due Date: November 17, 2021 Material Covered: Lessons 7 and 8

Notes:

- The solution to the assignment problems must contain all the calculations and details in support of the

answers. You may use statistical software to compute normal probabilities and percentiles where

necessary. - Copyright Notice: The present document and the contents thereof are the property and copyright of the

professor(s) who prepared it at Concordia University. No part of the present document may be used for

any purpose other than research or teaching purposes at Concordia University. Furthermore, no part of

the present document may be sold, reproduced, republished or disseminated in any manner or form

without the prior written permission of its owner and copyright holder.

Question 1. [Marks: 5+5]

A marble manufacturer advertises that its bags of marbles will contain 25% “milky-white” marbles. Suppose

that a bag containing 80 marbles is inspected. Let π denote the number of “milky white” marbles in this bag.

(a) What value should we expect for our sampling percentage (πΜ =

πΏ

π

) of milky-white marbles in

this bag? How many marbles would this be?

(b) What is the standard deviation (SD) of the number of “milky white” marbles in this bag and

what can you say about the range of πΏ using this SD?

Question 2. [Marks: 5]

In a recent poll of 900 randomly selected adults, 37% reported that they could not swim 25 metres (the length

of a typical gymnasium lap pool).

What is the margin of error, using a 95% confidence level, for estimating the true proportion of adults who

self-report that they cannot swim 25 metres? Round to the nearest thousandth.

Question 3. [Marks: 5]

Find the sample size needed in a survey of a large population if the margin of error for a 99% confidence

interval must be 0.03 (3 percentage points).

INTE 296/EC β Discover Statistics

FALL 2021

INTE 296 Assignment 3 Page 2

Question 4. [Marks: 10+5]

A health foods shop owner is wondering if his customers’ daily vitamin supplement habits are in the same

proportion as the general population of adults. The shop owner heard in a news report that 60% of all adults

reported that they took a daily vitamin. The shop owner believes that his customers have a greater proportion

of adults who take a daily vitamin, so he decides to conduct a hypothesis test using the following null and

alternative hypotheses: π»0: π = 0.6 πππ π»π΄: π > 0.6. The shop owner collected data from 50 randomly

selected customers and recorded that 45 of them use daily vitamin supplements.

(a) Compute the appropriate test statistic and find the p-value of the test and based on a 5% significance level.

Write a conclusion about the null hypothesis by interpreting the p-value. Be sure to clearly state the decision

regarding the null hypothesis.

(b) Verify the test statistic computations using technology. (Please provide the appropriate output).

Question 5. [Marks: 10 +5]

A researcher believes that children who attend elementary school in a rural setting have lower obesity rates

than children who attend elementary school in an urban setting. The researcher collects a random sample

from each population and records the proportion of children in each sample who are clinically obese. The data

is summarized in the table below. Assume that all conditions for proceeding with a two-sample test have been

met.

(a) Find the z-statistic (rounded to the nearest hundredth) and p-value (rounded to the nearest thousandth)

for this hypothesis test. Using a 5% significance level, state the correct conclusion regarding the null

hypothesis H0: prural = purban. [Set up the null and alternative hypotheses correctly and provide all the

steps of hypothesis testing in reaching your conclusion.]

(b) Verify the test statistic computations using technology. (Please provide the appropriate output).

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