1) A study investigated the effect of pandemic stress on students at two years colleges in New Jersey. The instrument used was the stress/depression scale with range 1 to 100. The normal mean score on this test is 75. It is well known that these scores follow a normal distribution with standard deviation of 12. This test was administered to a random sample of 30 students from the above population in the spring of 2020 and it was found that the average score was 80. Do we have an evidence that the scores are significantly higher after the pandemic? Perform the appropriate test at the 5% significance level, calculate (or appropriate) the p-value and comment on its strength of evidence against the null hypothesis. 2) A tennis racket company is testing the rackets. A Wimbledon champion requested an information about the platinum G-6 racket. The champion needs a racket which gives 85 mps first serve speed, which means 180 yards of the court. The company tested this racket using a ground launch system which measures distances at a given speed , and they gathered the data on 6 runs. Will this champion be satisfied with the tennis racket? Explain the meaning of Type 1 and 2 errors and power in the context of the problem. 3) A random sample of 28 student's final exam scores in statistics I, revealed a mean of 63.39 with a standard deviation of 25.17. It is assumed that the grades follow a normal distribution. The teacher believes that on the average his student's final exams are lower than C (70%). Explain the meaning of Type 1 and 2 errors and power in the context of the problem. 4) According to Communications Industry Forecast and Reports, the average person spent 5 hours a day on internet in 2019. In 2020, a random sample of 20 people gave the number of hours spent on internet. Do the data provide sufficient evidence to conclude that the amount of television watched per day has changed? Explain the meaning of Type 1 and 2 errors and power in the context of the problem. 5) It is believed that the levels of sulfate residuals obtained from photosynthesis of carbon- based substrates are less than 900 grams. To make sure the scientists in Fiji Islands took a random sample of 15 substrates and the following data was collected. Data representing the levels of sulfate residuals obtained from photosynthesis of carbon-based substrate, measured in grams, was collected. Explain the meaning of Type 1 and 2 errors and power in the context of the problem. Question taking longer to answer . Any clarity needed