Part BI The manager of a small business is thinking about establishing a new billing system for the customers. After a comprehensive nancial analysis, he concludes that the new system would be cost-effective only if the mean value of weekly accounts is greater than $50. A random sample of 46 weekly accounts is drawn for which the sample mean is $52, and sample standard deviation is $10. The manager believes that the accounts are normally distributed. Is there enough evidence at the 5% signicance level to conclude that the new system would be cost effective? (B1) State the parameter of interest and the null and alternative hypotheses. (1 mark) (B2) State the standardised test statistic and the sampling distribution of it under the null hypothesis. (1 mark} (B3) State the level of signicance. What does the level of signicance measure? Explain. (1 mark) (B4) State the decision rule with the test statistic method. (1 mark} (B5) Using the sample data, the manager comes up with the following two test outcomes. z-Test of a Mean Sample mean 52 z Stat 1.36 Population standard deviation 10 P[Z