The Bank of Canada plans to increase interest rates many times in 2022 [1]. Suppose a survey is conducted by a polling organization, and Saskatchewanians answered the question: “do you believe will you be majorly affected, somewhat affected, or not at all affected by interest rates climbing?”. The survey yielded the following results.

The same survey was conducted in Ontario, and it was found that 35% of Ontarians believed they would be majorly affected, 15% believed they would be somewhat affected, and 50% believed they would not be affected at all. The polling organization is interested in determining if there is a difference in the population proportions between the two provinces. Conduct an appropriate hypothesis test by filling in the blanks below. Let group 1 be the “majorly affected” group; group 2 be the “somewhat affected” group, and group 3 be the “not at all affected” group.

1) State the null and alternative hypotheses using the appropriate notation.

2) Calculate the test statistic. Please round your final answer to 2 decimal places. Note: you may use Excel to calculate the test statistic. No need to show your work.

3) Find the p-value using Excel. Use your rounded test statistic from part 2, and show your Excel command. For example, suppose this question had instead asked for you to calculate a sample mean of 10 values. If I had data in cells A1 through A10 in Excel, and I typed =average(A1:A10), hit enter, and got the result 10.2, then I would provide: =average(A1:A10)=10.2. Note: you will get a strange value here. Don’t worry about it.

4) Based on this p-value, do you reject the null hypothesis (answer “yes” or “no” only, with no additional words)?

5) In one sentence, conclude in the context of the original question.

6) Conduct a follow-up analysis. Show all of your work. Do exactly as shown in the M8 Tutorial (second picture), including all rounding (copy/paste from that document and change numbers and context). Ensure you have the entire follow-up analysis (i.e., everything on that page, not just the table).
$Step Apples Oranges Bananas Peaches 53 Grapefruit 79 1 391 202 275 - 0.053 × 0.05 :0.079 0.08 P1 = P2 = || P3 = 1000 = 0.275 - 0.28 = 0.391 - 0.39 0.202 z 0.20 1000 1000 1000 1000 0.39(1 – 0.39)' 0.2(1 – 0.2)\ 0.28(1 – 0.28)\ 0.05(1 – 0.05) 0.08(1 – 0.08) 0.08, 2 pz- N(0.2, P4~ N|0.05, P5~ N( P1 ~ N[ 0.39, P3~ 1000 1000 1000 1000 1000 P1~ N(0.39, 0.0154) P2~ N(0.2, 0.0126) P3~ N(0.28, 0.0142) P4~N(0.05, 0.0069) P5~ N(0.08, 0.0086) P1(1 – p1) P2(1 – p2) P3(1– p3) Þ4(1 – p4) P5(1 – ps) P5 ± za 3 Pit za P2± Za P3 ± Za 2V P4 ± Za n 0.39 ± 1.96(0.0154) 0.20 ± 1.96(0.0126) 0.28 ± 1.96(0.0142) 0.05 ± 1.96(0.0069) 0.08 ± 1.96(0.0086) z [0.35, 0.42] z [0.17, 0.23] z [0.25, 0.31] z [0.03, 0.07] z [0.06, 0.10] We can be 95% confident that the population proportion for apples (p1) lies between 0.35 and 0.42. In the null hypothesis, we hypothesized that p, was 0.36. We can be 95% confident that the population proportion for oranges (p2) We can be 95% confident that the We can be 95% confident that population proportion for bananas (p3) lies between 0.25 We can be 95% confident that the population proportion for grapefruit lies between 0.06 and 4 the population proportion for peaches (p4) lies between 0.03 lies between 0.17 and 0.23. and 0.31. and 0.07. 0.10. In the null hypothesis, we hypothesized that p2 was In the null hypothesis, we hypothesized that p5 was 0.08. Since 0.08 lies in the confidence confidence interval, 0.09 is not a interval, 0.08 is a plausible value of ps, so we would not reject the null hypothesis that p5 = 0.08. In the null hypothesis, we hypothesized that p3 was 0.21. In the null hypothesis, we hypothesized that p4 was 0.09. 5 Since 0.36 lies in the confidence 0.26. Since 0.26 does not lie Since 0.21 does not lie in the Since 0.09 does not lie in the interval, 0.36 is a plausible value in the confidence interval, of p1, so we would not reject the 0.26 is not a plausible value null hypothesis that p = 0.36. confidence interval, 0.21 is not a plausible value of p3, so we would plausible value of p4, so we reject the null hypothesis that p3 of p2, so we would reject the null hypothesis that p2 = 0.26. = 0.21. would reject the null hypothesis that p4 = 0.09. %3D All together, we can say that the city market shares are not different from the provincial market shares for apples and grapefruit. However, since the confidence intervals for oranges and peaches are entirely below their respective provincial market shares, the market shares for oranges and peaches in the city are less than the market share for oranges and peaches in the province as a whole. Additionally, since the confidence interval for bananas is entirely above the provincial market share, the city market share for bananas is greater than the provincial market share.$
Transcribed Image Text:Step Apples Oranges Bananas Peaches 53 Grapefruit 79 1 391 202 275 - 0.053 × 0.05 :0.079 0.08 P1 = P2 = || P3 = 1000 = 0.275 - 0.28 = 0.391 - 0.39 0.202 z 0.20 1000 1000 1000 1000 0.39(1 – 0.39)' 0.2(1 – 0.2)\ 0.28(1 – 0.28)\ 0.05(1 – 0.05) 0.08(1 – 0.08) 0.08, 2 pz- N(0.2, P4~ N|0.05, P5~ N( P1 ~ N[ 0.39, P3~ 1000 1000 1000 1000 1000 P1~ N(0.39, 0.0154) P2~ N(0.2, 0.0126) P3~ N(0.28, 0.0142) P4~N(0.05, 0.0069) P5~ N(0.08, 0.0086) P1(1 – p1) P2(1 – p2) P3(1– p3) Þ4(1 – p4) P5(1 – ps) P5 ± za 3 Pit za P2± Za P3 ± Za 2V P4 ± Za n 0.39 ± 1.96(0.0154) 0.20 ± 1.96(0.0126) 0.28 ± 1.96(0.0142) 0.05 ± 1.96(0.0069) 0.08 ± 1.96(0.0086) z [0.35, 0.42] z [0.17, 0.23] z [0.25, 0.31] z [0.03, 0.07] z [0.06, 0.10] We can be 95% confident that the population proportion for apples (p1) lies between 0.35 and 0.42. In the null hypothesis, we hypothesized that p, was 0.36. We can be 95% confident that the population proportion for oranges (p2) We can be 95% confident that the We can be 95% confident that population proportion for bananas (p3) lies between 0.25 We can be 95% confident that the population proportion for grapefruit lies between 0.06 and 4 the population proportion for peaches (p4) lies between 0.03 lies between 0.17 and 0.23. and 0.31. and 0.07. 0.10. In the null hypothesis, we hypothesized that p2 was In the null hypothesis, we hypothesized that p5 was 0.08. Since 0.08 lies in the confidence confidence interval, 0.09 is not a interval, 0.08 is a plausible value of ps, so we would not reject the null hypothesis that p5 = 0.08. In the null hypothesis, we hypothesized that p3 was 0.21. In the null hypothesis, we hypothesized that p4 was 0.09. 5 Since 0.36 lies in the confidence 0.26. Since 0.26 does not lie Since 0.21 does not lie in the Since 0.09 does not lie in the interval, 0.36 is a plausible value in the confidence interval, of p1, so we would not reject the 0.26 is not a plausible value null hypothesis that p = 0.36. confidence interval, 0.21 is not a plausible value of p3, so we would plausible value of p4, so we reject the null hypothesis that p3 of p2, so we would reject the null hypothesis that p2 = 0.26. = 0.21. would reject the null hypothesis that p4 = 0.09. %3D All together, we can say that the city market shares are not different from the provincial market shares for apples and grapefruit. However, since the confidence intervals for oranges and peaches are entirely below their respective provincial market shares, the market shares for oranges and peaches in the city are less than the market share for oranges and peaches in the province as a whole. Additionally, since the confidence interval for bananas is entirely above the provincial market share, the city market share for bananas is greater than the provincial market share.
Transcribed Image Text:Assignment Questions The Bank of Canada plans to increase interest rates many times in 2022 [1]. Suppose a survey is conducted by a polling organization, and Saskatchewanians answered the question: "do you believe will you be majorly affected, somewhat affected, or not at all affected by interest rates climbing?". The survey yielded the following results. Majorly affected 3600 Somewhat affected Not at all affected 1200 5000 The same survey was conducted in Ontario, and it was found that 35% of Ontarians believed they would be majorly affected, 15% believed they would be somewhat affected, and 50% believed they would not be affected at all. The polling organization is interested in determining if there is a difference in the population proportions between the two provinces. Conduct an appropriate hypothesis test by filling in the blanks below. Let group 1 be the "majorly affected" group; group 2 be the "somewhat affected" group, and group 3 be the “not at all affected" group. 1) State the null and alternative hypotheses using the appropriate notation. 2) Calculate the test statistic. Please round your final answer to 2 decimal places. Note: you may use Excel to calculate the test statistic. No need to show your work. 3) Find the p-value using Excel. Use your rounded test statistic from part 2, and show your Excel command. For example, suppose this question had instead asked for you to calculate a sample mean of 10 values. If I had data in cells Al through A10 in Excel, and I typed =average(A1:A10), hit enter, and got the result 10.2, then I would provide: =average(Al:A10)=10.2. Note: you will get a strange value here. Don't worry about it.

Question

The Bank of Canada plans to increase interest rates many times in 2022 [1]. Suppose a survey is conducted by a polling organization, and Saskatchewanians answered the question: “do you believe will you be majorly affected, somewhat affected, or not at all affected by interest rates climbing?”. The survey yielded the following results.

The same survey was conducted in Ontario, and it was found that 35% of Ontarians believed they would be majorly affected, 15% believed they would be somewhat affected, and 50% believed they would not be affected at all. The polling organization is interested in determining if there is a difference in the population proportions between the two provinces. Conduct an appropriate hypothesis test by filling in the blanks below. Let group 1 be the “majorly affected” group; group 2 be the “somewhat affected” group, and group 3 be the “not at all affected” group.

1) State the null and alternative hypotheses using the appropriate notation.

2) Calculate the test statistic. Please round your final answer to 2 decimal places. Note: you may use Excel to calculate the test statistic. No need to show your work.

3) Find the p-value using Excel. Use your rounded test statistic from part 2, and show your Excel command. For example, suppose this question had instead asked for you to calculate a sample mean of 10 values. If I had data in cells A1 through A10 in Excel, and I typed =average(A1:A10), hit enter, and got the result 10.2, then I would provide: =average(A1:A10)=10.2. Note: you will get a strange value here. Don’t worry about it.

4) Based on this p-value, do you reject the null hypothesis (answer “yes” or “no” only, with no additional words)?

5) In one sentence, conclude in the context of the original question.

6) Conduct a follow-up analysis. Show all of your work. Do exactly as shown in the M8 Tutorial (second picture), including all rounding (copy/paste from that document and change numbers and context). Ensure you have the entire follow-up analysis (i.e., everything on that page, not just the table).

Step
Apples
Oranges
Bananas
Peaches
53
Grapefruit
79
1
391
202
275
- 0.053 × 0.05
:0.079 0.08
P1 =
P2 =
||
P3 =
1000
= 0.275 - 0.28
= 0.391 - 0.39
0.202 z 0.20
1000
1000
1000
1000
0.39(1 – 0.39)'
0.2(1 – 0.2)\
0.28(1 – 0.28)\
0.05(1 – 0.05)
0.08(1 – 0.08)
0.08,
2
pz- N(0.2,
P4~ N|0.05,
P5~ N(
P1
~ N[ 0.39,
P3~
1000
1000
1000
1000
1000
P1~ N(0.39, 0.0154)
P2~ N(0.2, 0.0126)
P3~ N(0.28, 0.0142)
P4~N(0.05, 0.0069)
P5~ N(0.08, 0.0086)
P1(1 – p1)
P2(1 – p2)
P3(1– p3)
Þ4(1 – p4)
P5(1 – ps)
P5 ± za
3
Pit za
P2± Za
P3 ± Za
2V
P4 ± Za
n
0.39 ± 1.96(0.0154)
0.20 ± 1.96(0.0126)
0.28 ± 1.96(0.0142)
0.05 ± 1.96(0.0069)
0.08 ± 1.96(0.0086)
z [0.35, 0.42]
z [0.17, 0.23]
z [0.25, 0.31]
z [0.03, 0.07]
z [0.06, 0.10]
We can be 95% confident that
the population proportion for
apples (p1) lies between 0.35
and 0.42.
In the null hypothesis, we
hypothesized that p, was 0.36.
We can be 95% confident
that the population
proportion for oranges (p2)
We can be 95% confident that the We can be 95% confident that
population proportion for
bananas (p3) lies between 0.25
We can be 95% confident that
the population proportion for
grapefruit lies between 0.06 and
4
the population proportion for
peaches (p4) lies between 0.03
lies between 0.17 and 0.23.
and 0.31.
and 0.07.
0.10.
In the null hypothesis, we
hypothesized that p2 was
In the null hypothesis, we
hypothesized that p5 was 0.08.
Since 0.08 lies in the confidence
confidence interval, 0.09 is not a interval, 0.08 is a plausible value
of ps, so we would not reject the
null hypothesis that p5 = 0.08.
In the null hypothesis, we
hypothesized that p3 was 0.21.
In the null hypothesis, we
hypothesized that p4 was 0.09.
5
Since 0.36 lies in the confidence
0.26. Since 0.26 does not lie
Since 0.21 does not lie in the
Since 0.09 does not lie in the
interval, 0.36 is a plausible value in the confidence interval,
of p1, so we would not reject the 0.26 is not a plausible value
null hypothesis that p = 0.36.
confidence interval, 0.21 is not a
plausible value of p3, so we would plausible value of p4, so we
reject the null hypothesis that p3
of p2, so we would reject the
null hypothesis that p2 = 0.26. = 0.21.
would reject the null hypothesis
that p4 = 0.09.
%3D
All together, we can say that the city market shares are not different from the provincial market shares for apples and grapefruit. However, since the confidence intervals for oranges and peaches
are entirely below their respective provincial market shares, the market shares for oranges and peaches in the city are less than the market share for oranges and peaches in the province as a
whole. Additionally, since the confidence interval for bananas is entirely above the provincial market share, the city market share for bananas is greater than the provincial market share.

Assignment Questions
The Bank of Canada plans to increase interest rates many times in 2022 [1]. Suppose a survey
is conducted by a polling organization, and Saskatchewanians answered the question: "do
you believe will you be majorly affected, somewhat affected, or not at all affected by interest
rates climbing?". The survey yielded the following results.
Majorly affected
3600
Somewhat affected
Not at all affected
1200
5000
The same survey was conducted in Ontario, and it was found that 35% of Ontarians believed
they would be majorly affected, 15% believed they would be somewhat affected, and 50%
believed they would not be affected at all. The polling organization is interested in
determining if there is a difference in the population proportions between the two provinces.
Conduct an appropriate hypothesis test by filling in the blanks below. Let group 1 be the
"majorly affected" group; group 2 be the "somewhat affected" group, and group 3 be the “not
at all affected" group.
1) State the null and alternative hypotheses using the appropriate notation.
2) Calculate the test statistic. Please round your final answer to 2 decimal places. Note: you
may use Excel to calculate the test statistic. No need to show your work.
3) Find the p-value using Excel. Use your rounded test statistic from part 2, and show your
Excel command. For example, suppose this question had instead asked for you to calculate a
sample mean of 10 values. If I had data in cells Al through A10 in Excel, and I typed
=average(A1:A10), hit enter, and got the result 10.2, then I would provide:
=average(Al:A10)=10.2. Note: you will get a strange value here. Don't worry about it.

Accepted Answer

a) The test wants to see if the population proportion differs between the two provinces.
Thus, we…