Good day,

I hope you are well.

I am struggling with the concepts of significance. Could you please assist me in providing explanations and answers to the following practice questions individually.

I look forward to your reply.

Your assistance is greatly appreciated.

Kind regards.

1. According to "Dietary Goals for the United States (1997)", high sodium intake may be related to ulcers, stomach cancer, and migraine headaches. The human requirement for salt is only 220 milligram per day, which is surpassed in most single servings of ready-to-eat cereals. If a random sample of 20 similar servings of Special K has a mean sodium content of 244 milligrams and a standard deviation 24,5 milligrams does this suggest at 0,01 level of significance that the average sodium content for single servings of Special K is greater than 220 milligrams? Assume the distribution of sodium content to be normal. 2. In a research report by a medical school, it is claimed that mice with an average life span of 32 months will live to be about 40 months old when 40% of the calories in their food are replaced by vitamins and protein. Is there any reason to believe that the mean life time is smaller than 40 months if 64 mice that are placed on this diet gave an average life of 38 months with a standard deviation of 5,8 months? Use a 0,025 level of significance. 3. In a research report by a medical school, it is claimed that mice with an average life span of 32 months will live to be about 40 months old when 40% of the calories in their food are replaced by vitamins and protein. Is there any reason to believe that the mean life time differs from 40 months if 64 mice that are placed on this diet gave an average life of 38 months with a standard deviation of 5,8 months? Use a 0,1 level of significance. 4. A farmer wishes to investigate if a new variety of wheat is more susceptible to a disease than an old variety. It is known that this disease strikes approximately 15% of all wheat plants. A field experiment was conducted, and of 120 new plants, 90 become infected. Can the farmer conclude at a 10% significance level that more than 15% of the plants were infected? 5. A beer company uses dispensing to fill beer cans that provide a maximum variance of 5ml so that cans are not overfilled or under filled. A sample of fills for 25 cans yielded a variance of 7ml. If the amounts of beer dispensed are normally distributed, test at the 5% significance level whether the population variance differs from the maximum variance provided