Question: Aiming to boost the economy within rural areas of Ontario, the governm

Question

Question: Aiming to boost the economy within rural areas of Ontario, the government invested on a new initiative, named Canada Rural Partnership (CRP). Two consultancies won the bid to undertake this project: Innovation Pursuit (IP) and North Consultancy (NC). IP supported far northern communities and NC supported rural areas. IP and NC's goal were to: Initiate collaboration between rural communities and stakeholders to address barriers and challenges to local development Prepare information and tools used by rural communities and regions to develop local amenities and other assets Initiate new economic activities in rural Canada During four years they provided advice to 653 clients. At this point of time the government of Ontario is evaluating CRP's effectiveness. They would like to know the following based on a sample of 150 companies. Clients who participated in this program were asked to identify their level of satisfaction with the government prior to receiving consultation; this showed a mean of <3. The government of Ontario likes to know whether their opinion has risen to more than 3 after the consultation with 5% significance. Clients were provided with 1) one to one consultation, 2) workshops and 3) information packages 4) Funding. The government of Ontario is interested to know which one of these methods were deemed most useful by clients, analyze (hint: compare mean with 95% confidence). Some of the employees of the Ontario government believe that IP performed better than NC. In the selected sample IP provided advice to 75 companies and NC to the rest of the 75 companies. Did IP really performed better than NC? - Analysis: For each question propose hypothesis, justify the selected method of analysis, discuss test requirements and present the test results in tables. - For each question discuss the findings of the study, what do they mean? how can they help in decision making? Data Set: https://docs.google.com/spreadsheets/d/1E23KDqF4wSBGj-aTak1mduTp5sLspIfrrxH_Gb_htWw/pubhtml

Explanation / Answer

Solution:

First of all we have to check the Governments claim. The government of Ontario likes to know whether their opinion has risen to more than 3 after the consultation with 5% significance.

Here, we have to check whether the average is more than 3 or not by using the one sample t test.

Null hypothesis: H0: µ = 3 versus alternative hypothesis: Ha: µ > 3

We are given, level of significance = alpha = 0.05

The test statistic formula is given as below:

Test statistic = t = ( X – mean) / [SD/sqrt(n)]

The test is given as below:

t Test for Hypothesis of the Mean

Data

Null Hypothesis                m=

3

Level of Significance

0.05

Sample Size

150

Sample Mean

3.240466667

Sample Standard Deviation

0.916033422

Intermediate Calculations

Standard Error of the Mean

0.0748

Degrees of Freedom

149

t Test Statistic

3.2151

Upper-Tail Test

Upper Critical Value

1.6551

p-Value

0.0008

Reject the null hypothesis

Here, we get the p-value as 0.0008 which is less than the given level of significance 0.05, so we reject the null hypothesis that population average opinion satisfaction score is 3. This means we conclude that the population average opinion satisfaction score is increased more than 3.

Now, government wants to compare all the methods given in the data sets. For comparing all the methods in the data sets, we need to use the one way analysis for variances or ANOVA.

The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: There is no significant difference in the averages for scores for different methods.

Alternative hypothesis: Ha: There is a significant difference in the averages for scores for different methods.

The significance level is given as 5% or alpha = 0.05.

The one way ANOVA is given as below:

ANOVA: Single Factor

SUMMARY

Groups

Count

Sum

Average

Variance

One to One Consultation

150

449.83

2.998866667

0.8304

Workshops

150

475.26

3.1684

0.8443

Information Packages

150

491.3

3.275333333

0.8625

Funding

150

530.1

3.534

0.8486

Clients Satisfaction with Government after Receiving Consultation

150

486.07

3.240466667

0.8391

IP's Performance

75

241.99

3.226533333

0.8566

NC's Performance

75

244.08

3.2544

0.8325

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

22.6649

6

3.7775

4.4709

0.0002

2.1087

Within Groups

754.5019

893

0.8449

Total

777.1668

899

Level of significance

0.05

Here, we get the p-value less than the given level of significance so we reject the null hypothesis that there is no significant difference in the averages for scores for different methods. This means we concluded that there is a significant difference in the averages for scores for different methods.

t Test for Hypothesis of the Mean

Data

Null Hypothesis                m=

3

Level of Significance

0.05

Sample Size

150

Sample Mean

3.240466667

Sample Standard Deviation

0.916033422

Intermediate Calculations

Standard Error of the Mean

0.0748

Degrees of Freedom

149

t Test Statistic

3.2151

Upper-Tail Test

Upper Critical Value

1.6551

p-Value

0.0008

Reject the null hypothesis

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