Television In the Pew Research social media survey, television viewers were asked if it would be very hard to give up watching television. In 2002, 38 % responded yes. In 2018, 31 % said it would be very hard to give up watching television. a. Assume that both polls used samples of 200 people. Do a test to see whether the proportion of people who reported it would be very hard to give up watching television was significantly different in 2002 and 2018 using a 0.05 significance level. b. Repeat the problem, now assuming the sample sizes were both 2000. (The actual sample size in 2018 was 2002.) c. Comment on the effect of different sample sizes on the p-value and on the conclusion.
Television In the Pew Research social media survey, television viewers were asked if it would be very hard to give up watching television. In 2002, 38 % responded yes. In 2018, 31 % said it would be very hard to give up watching television. a. Assume that both polls used samples of 200 people. Do a test to see whether the proportion of people who reported it would be very hard to give up watching television was significantly different in 2002 and 2018 using a 0.05 significance level. b. Repeat the problem, now assuming the sample sizes were both 2000. (The actual sample size in 2018 was 2002.) c. Comment on the effect of different sample sizes on the p-value and on the conclusion.
Solution Summary: The author explains how to determine whether the proportion of people who gave up watching television was significantly different in 2002 and 2018 at 5% significance level.
Television In the Pew Research social media survey, television viewers were asked if it would be very hard to give up watching television. In 2002,
38
%
responded yes. In 2018,
31
%
said it would be very hard to give up watching television.
a. Assume that both polls used samples of 200 people. Do a test to see whether the proportion of people who reported it would be very hard to give up watching television was significantly different in 2002 and 2018 using a
0.05
significance level.
b. Repeat the problem, now assuming the sample sizes were both 2000. (The actual sample size in 2018 was 2002.)
c. Comment on the effect of different sample sizes on the p-value and on the conclusion.
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
Morningstar tracks the total return for a large number of mutual funds. The following table shows the total return and the number of funds for four categories of mutual funds.
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DATA file
Type of Fund
Domestic Equity
Number of Funds
Total Return (%)
9191
4.65
International Equity
2621
18.15
Hybrid
1419
2900
11.36
6.75
Specialty Stock
a. Using the number of funds as weights, compute the weighted average total return for these mutual funds. (to 2 decimals)
%
b. Is there any difficulty associated with using the "number of funds" as the weights in computing the weighted average total return in part (a)? Discuss. What else might be used for weights?
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c. Suppose you invested $10,000 in this group of mutual funds and diversified the investment by placing $2000 in Domestic Equity funds, $4000 in International Equity funds, $3000 in Specialty Stock…
The days to maturity for a sample of five money market funds are shown here. The dollar amounts invested in the funds are provided.
Days to
Maturity
20
Dollar Value
($ millions)
20
12
30
7
10
5
6
15
10
Use the weighted mean to determine the mean number of days to maturity for dollars invested in these five money market funds (to 1 decimal).
days
c. What are the first and third quartiles?
First Quartiles (to 1 decimals)
Third Quartiles (to 4 decimals)
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Which companies spend the most money on advertising? Business Insider maintains a list of the top-spending companies. In 2014, Procter & Gamble spent more than any other company, a whopping $5 billion. In second place was Comcast, which spent $3.08 billion (Business Insider website, December 2014). The top 12 companies and
the amount each spent on advertising in billions of dollars are as follows.
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DATA file
Company
Procter & Gamble
Comcast
Advertising
($billions)
$5.00
3.08
2.91
Company
American Express
General Motors
Advertising
($billions)
$2.19
2.15
ETET
AT&T
Ford
Verizon
L'Oreal
2.56
2.44
2.34
Toyota
Fiat Chrysler
Walt Disney Company
J.P Morgan
a. What is the mean amount spent on advertising? (to 2 decimals)
2.55
b. What is the median amount spent on advertising? (to 3 decimals)
2.09
1.97
1.96
1.88
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