The price of a standard health insurance is 1,500 per year. An insurance company is interested...

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The price of a standard health insurance is €1,500 per year. An insurance company is interested to know if it should offer this insurance for this price as a new service to its clients. Re-search has shown that this will be profitable if the average yearly health costs per client are less than €1,200. To investigate the average yearly health costs per client, the company has randomly selected 25 clients. The average costs of these clients are €1,100 per year. Suppose that the yearly costs per client are normally distributed but that the standard deviation is not known. The sample standard deviation of the 25 selected clients appears to be €300. Perform a test (at a 5% significance level) to investigate whether it is profitable to offer the health insurance. (Hint. You may draw a conclusion as follows: we should decide not to offer the insurance, because it is not profitable.) The price of a standard health insurance is €1,500 per year. An insurance company is interested to know if it should offer this insurance for this price as a new service to its clients. Re-search has shown that this will be profitable if the average yearly health costs per client are less than €1,200. To investigate the average yearly health costs per client, the company has randomly selected 25 clients. The average costs of these clients are €1,100 per year. Suppose that the yearly costs per client are normally distributed but that the standard deviation is not known. The sample standard deviation of the 25 selected clients appears to be €300. Perform a test (at a 5% significance level) to investigate whether it is profitable to offer the health insurance. (Hint. You may draw a conclusion as follows: we should decide not to offer the insurance, because it is not profitable.)