# Z Test for A Population Proportion Statistics Questions

Description

Question 3
Not yet saved
Marked out of 7.00
The COVID-19 pandemic accelerated the shift from cash to cards. The use of contactless payments also increased sharply in 2020,
and lockdowns boosted the growth of e-commerce. Australian Beaurea of Statistics (ABS) claims that 27% of Australian consumers
used Paypal when shopping online, and 62.1% of Australians used Amazon pay, with the remainder of Australians using Credit or
Debit cards.
When randomly surveying 145 Australian online shoppers, 24 reported using Paypal, 64 said using Amazon pay, while 57 used
either a Credit or a Debit card.
The observed and expected data are summarised in the table below:
Online payment methods
Observed
Expected
(O-E)^2/E
Paypal
24
***
5.863
Amazon pay
64
90.045
***
Credit/Debit cards
57
15.805
107.373
Use the above information to answer the following questions by choosing the most correct option or typing the answer.
1. (1 mark) What is the expected value for Australians who used Paypal?
(2dp)
2. (1 mark) What is the contribution to chi-squared for Amazon pay?
(3dp)
3. (1 mark) What is the chi-squared test statistic?
(3dp)
4. (2 marks) Using Excel to find the p-value associated with the chi-squared test, what is your conclusion about the ABS’s claim?
A. Yes, we reject the null hypothesis, and all proportions are different to what ABS has stated.
B. No, we do not reject the null hypothesis.
C. Yes, we reject the null hypothesis, and at least one of the proportions is different to what ABS has stated.
Now, we are interested in Paypal users versus non-Paypal users.
Research Question: Is the proportion of Paypal users different from the ABS’s claim of 0.27? (Hint: To answer this research
question, you may need to conduct a different hypothesis test)
5. (1 mark) What is the absolute value of the test statistic?
(3dp)
6. (1 mark) Is it reasonable to conclude that the proportion of Paypal users is significantly different to 0.27?
A. Yes, we can conclude that the proportion of Paypal users is significantly different, and specifically the proportion is likely to be
higher.
B. Yes, we can conclude that the proportion of Paypal users is significantly different, and specifically the proportion is likely to be
lower.
C. No, we cannot conclude that the proportion of Paypal users is significantly different.
Copyright © Macquarie University. Copying or distribution of part or all of the contents in any form is prohibited.