Question

1. There are many ways to measure the reading ability of children. Research designed to improve reading performance is dependent on good measures of the outcomes. One frequently-used test is the DRP, or Degree of Reading Power. It is known that the distribution of DRP scores is normally distributed. A researcher suspects that the mean score µ of all third-graders in Henrico County Schools is different from the national mean, which is 32. To test her suspicion, she administers the DRP to a random sample of 22 Henrico County third-grade students. Their scores are recorded in the following table:

40 26 39 17 42 18 24 43 46 27 19

47 19 26 37 34 15 45 41 39 31 46

(a) Find the t critical value for a 90% confidence interval for the true mean, µ, of the population.

(b) State and verify the conditions for the confidence interval.

(c) Compute and interpret the 90% confidence interval for the mean DRP score in Henrico County Schools. (You can find your point estimate and standard error in your calculator using the 1-Var Stats function. Compare your answers with a classmate to make sure you entered things in correctly!)

(d) Use the confidence interval you constructed in Part (c) to comment on whether you agree with the researcher’s suspicion. Explain your reasoning clearly.

2. Paddy’s Pub in South Philadelphia sponsored a sample survey of 500 randomly-selected customers to get feedback on the new items they added to their menu over the summer. One question the survey asked was,“Did you try one of our new specialty drinks this summer?” Of the 500 customers who took the survey, 421 answered “Yes.”

(a) Construct and interpret a 95% confidence interval for the proportion of all Paddy’s Pub customers who tried one of the pub’s new drinks this summer. Clearly specify your z critical value.

(b) In order to promote the popularity of the new menu items, the owners at Paddy’s begin advertising that 86% of customers ordered the new specialty drinks this summer. Use the confidence interval you constructed in Part (a) to comment on whether you agree with their claim. Explain your reasoning clearly

Answer #1

Answer 2)

Given Point estimate P = 421/500 = 0.842

N = 500

First we need to check the conditions of normality

That is if n*p and n*(1-p) both are greater than 5 or not

N*p = 421

And n*(1-p) = 79

As both are greater than 5

We can use standard normal z table to estimate the interval

For 95% confidence level, critical value z from z table is 1.96

Margin of error (MOE) = Z*√{p*(1-p)/n}

MOE = 0.0319709586218

Confidence interval is given by

P-MOE < P < P+MOE

0.8100290413781 < P < 0.8739709586218

B)

Yes i agree with the claim as the confidence interval contains the value 0.86 (86%).

There are many ways to measure the reading ability of children.
Research designed to improve reading performance is dependent on
good measures of the outcomes. One frequently-used test is the DRP,
or Degree of Reading Power. It is known that the distribution of
DRP scores is normally distributed. A researcher suspects that the
mean score µ of all third-graders in Henrico County Schools is
different from the national mean, which is 32. To test her
suspicion, she administers the DRP...

In a July 2001 research note, the U.S. Department of
Transportation reported the results of the National Occupant
Protection Use Survey. One focus of the survey was to determine the
level of cell phone use by drivers while they are driving a motor
passenger vehicle. Data collected by observers at randomly selected
intersection across the country revealed that in a sample of 1165
drivers, 35 were using their cell phone.
(a) Check and verify the two conditions for a 98%...

In February 2012, the Pepsi Next product was launched into
the US market. This case study provides students with an
interesting insight into PepsiCo’s new product process and some of
the challenging decisions that they faced along the way.
Pepsi Next Case Study
Introduction
Pepsi Next was launched by PepsiCo into the US market in
February 2012, and has since been rolled out to various
international markets (for instance, it was launched in Australia
in September 2012).
The new product...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 11 minutes ago

asked 24 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago