Suppose you work for an investment rm that is interested in building a new shopping center in suburban Brisbane. Previous experience indicates that shopping centers such as these are only successful if the average disposable income of households in the surrounding suburbs exceeds $260 per week. A research assistant has drawn a random sample of 31 households in the area and found a sample mean of $272 per week with a standard deviation of $58. Using a 5 percent level of significance, test whether the population mean exceeds $260 based upon the information given. i. State the data type and parameter of interest. Data type: Parameter of interest: ii. State the Null and Alternative hypotheses: HO: HA: iii. State the test statistic, the sampling distribution of the standardised test statistic and the level of significance. Verify the required conditions. Test statistic: Standardised test statistic: Distribution of the standardised test statistic: Levei of significance: Verification of the required conditions: iv. State the decision rule: v. Calculate the sample value of the test statistic and the pvalue. { You can either manually calculate or select the correct output and obtain the values) z-Test of a Mean _M_ Population standard deviation P(Z