I would like some assistance with the following hypothesis testing questions

I would like some detailed explanation

Question 4 (Total = 20 marks) The following questions relate to Hypothesis Testing. A. A manufacturer of sprinkler systems used for fire protection in office buildings claims that the true average system-activation temperature is 130 degrees. A sample of 9 systems when tested yields a sample average activation temperature of 131.08 degrees. If the distribution of activation times is normal with a standard deviation of 1.5 degrees, test at the 1% level of significance to see if the data shows evidence which is different from the manufacturers claim. (a) State the null and alternative hypotheses to be tested. (2 marks) Ho:(b) What is the test statistic? (1 mark) (c) What is the critical region? Show this graphically. (2 marks) (d) Evaluate the test statistic. (3 marks)(e) Should we reject or fail to reject the null hypothesis? Please give reasonable proof to support your answer. (I mark) \\ (f) State your. conclusion in the context of the problem. (I mark) B. The records of a stateowned company indicate that of all vehicles undergoing emissions testing during the previous year, 70% passed on the rst test. A random sample of 200 cars tested in the country during the current year reveals that 62% passed the initial test. Does this data suggest that the true proportion for this country is less than the previous countrywide proportion? Test the relevant hypothesis at the 5% level of signicahce (a) State the null and alternative hypotheses to be tested. (2 "lurks? H0: H1: (b) What is the test statistic? (I mark) (c) What is the critical region? Show this graphically. (2 marks) \f(e) Should we reject or fail to reject the null hypothesis? Please give reasonable proof to support your answer. (I mark) (f) State your conclusion in the context of the problem. (1 mark) Question 4 (Total = 20 marks) The following questions relate to Hypothesis Testing. A. Total blood volume (in ml) per body weight (in kg) is important in medical research/ for healthy adults, the red blood cell volume mean is about 28 ml/kg. Red blood cells that is too low or too high can indicate a medical. Suppose that Roger has seven blood tests and averages 32.7 ml/kg per test. Suppose also that red blood cell volume follows a normal distribution with a standard deviation of4.75ml/kg. At the 5% level of significance, test that the mean blood cell volume is different from 28ml/kg. (a) State the null and alternative hypotheses to be tested. (2 marks) Ho: (b) What is the test statistic? (1 mark)(c) What is the critical region? (2 marks) 10 (d) Evaluate the test statistic. (3 marks) (e) Should the null hypothesis be accepted or rejected? Please give reasonable proof to support your answer. (I mark) (1) State your conclusion in the context of the problem. (I mark) B. Government officials claim that at least 85% of the public-sector workers have graduated from school and received at a university degree or are currently enrolled in a degree program. A random sample of 60 employees shows that 47 have received or are enrolled in a degree program. The minister believes that the officials are incorrect the figure is less. Test to see if the data agrees with the minister or with government officials at the 5% level (a) State the null and alternative hypotheses to be tested. (2 marks) Ho: H1: 11 (b) What is the test statistic? (1 mark)(c) What is the critical region? (2 marks) ((1) Evaluate the test statistic. (3 marks) (e) Should the null hypothesis be accepted or rejected? Please give reasonable proof to support your answer. (I mark) 12 (1) State your conclusion in the context of the problem. (I mark)