1. The manager at Bell's Gym wants to know the proportion of members who use the Cardio Machines. A sample of 260 members showed that 40 of them use cardio machines. Calculate a 97% confidence interval for the proportion of members who use the cardio machines. 2. A farmer grows a new variety of potatoes. A random sample of 80 roots of the new variety is harvested and weighed. The mean weight was found to be 3.20 per root, and the standard deviation of 0.50 kg per root. Based on his knowledge of the land, the farmer expected 3.30kg per root You are required to test at the 5% level whether the sample provides sufficient evidence that the crop is NOT what the farmer expected. a) State, in symbols, appropriate null and alternative hypothesis for the test. b) Determine the critical value(s) for the test. c) Calculate the value of the test statistic. d) State your Decision and Conclusion, giving a reason for your answer.

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