Question

Horizon Research recently published the report "Generation Kiwisaver-Securing the Future of Young New Zealanders" which was based on a public opinion survey completed in July 20172. The survey was conducted online with a nationally-representative sample of New Zealanders aged 18 years or over (adult New Zealanders). You may assume that the survey used simple random sampling One question in the survey asked the respondents where they sought financial advice. Note: t was possible to choose more than one source of advice The table below shows from where the respondents sought their advice according to their age group. 18 to 34 35 to 64 65 years or Advice from years years over n 463 n 1163 n 503 An independent financial adviser 65 209 8 6 A financial adviser in a bank 79 151 65 Tools and calculators fr㎝ my provider 83 163 15 302 Friends and family 213 70 105 My lawyer or accountant 50 None of the sources listed (above) 167 582 292 (a) State the sampling situation for analysing the difference between the estimated proportion of New Zealanders aged 35 to 64 years who, in July 2017, sough:financial advice from an independent adviser and the estimated proportion of New Zealanders 65 years and over who, in July 2017 did so [1 mark ] b) Carry out a t-test to investigate whether there is a difference between the under lying proportion of New Zealanders aged 18 to 34 years who, in July 2017, sought financial advice from friends and family and the underlying proportion of New Zealanders aged 18 to 34 years who, in July 2017, did not seek financial advice from the sources listed (none of the sources listed) I 8 marks] Notes: 0) Refer to the instructions on Page 1 of this assignment: "Hypothesis tests in this assign i) You must clearly show that you have followed the "Step-by-Step Guide to Performing a Hypothesis Test by Hand" given in the Lecture Workbook, Page 12, Chapter 7 ii) At Steps 5and 8 it is necessary to use the t-procedures tool on Canvas to determine the standard error and the t-multiplier. Look under Assignments → Assignment 3 iv) At Step 6 it is necessary to use either the t-procedures tool on Canvas, a graphics calculator, SPSS, or Excel to determine the P-value (c) Does the confidence interval given in part (b)contain the true value of the parameter? Briefly explain. 1 mark

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Answer 1

(a) The sampling situation for analyzing the difference of the estimated proportions of persons who took financial advice from an independent advisor in between the age groups of persons 35 to 64 years and 65 years and over is as follows:

Here, a simple random nationality representative sample of New Zealandars of size n1 = 1163 persons have been selected from the age group of persons 35 to 64 years and among which, x1 = 209 persons sought financial advice from an independent advisor with their estimated proportion p1 = x1/n1 = 209/1163 = 0.1797

Also, another simple random nationality representative sample of New Zealandars of size n2 = 503 persons have been selected from the age group of persons 65 years and over and among which, x2 = 86 persons sought financial advice from an independent advisor with their estimated proportion p2 = x2/n2 = 86/503 = 0.1709.

Then it is required to test the significant difference between the above p1 and p2.

(b) Here we have to test the significant difference between the estimated proportions of persons who sought financial advise from friends and family and who did not seek financial advise from the sources listed from the persons of age group 18 to 34 years.

Taking x1 =Number of persons sought financial advise from friends and family from the persons of age group 18 to 34 years = 213

x2 =Number of persons did not seek financial advise from the sources listed from the persons of age group 18 to 34 years = 167

n =sample number of persons of age group 18 to 34 years = 463

Now we have to test (1) H0:p1=p2 against H1:p1is not equal to p2

(2) p1 = x1/n= 213/463 = 0.46 = 46% and p2 = x2/n= 167/463 = 0.36 = 36%

(3) calculated t test statistic value = 4.317

(4) p value = 0.000

(5) Since the calculated t value 0.000 is less than the level of significance 0.05, we reject H0 and conclude that there is a significant difference between the estimated proportions of persons who sought financial advise from friends and family and who did not seek financial advise from the sources listed from the persons of age group 18 to 34 years.

(6) The 95% confidence interval for the significant difference of proportions is (5.46%, 14.53%)

(C ) Since, H0 was rejected and there is a significant difference between p1 and p2 as 46% - 36% = 10%.

As 5.46%<10%< 14.53%, therefore, the 95% confidence interval for the difference in population parameters proportions (5.46%, 14.53%) contains the significant difference of 10% in population parameters proportions. That is the above confidence interval contains true significant difference value of the parameter.