A report by the Gallup Poll found that a woman visits her doctor, on average, at most 5.8 times each year. A random sample of 20 women results in these yearly visit totals. 3; 2; 1; 4; 7; 3; 9; 4; 6; 6; 8; 0; 5; 6; 5; 2; 1; 3; 4; 1 At the a = 0.05 level can it be concluded that the sample mean is higher than 5.8 visits per year? Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) State the null hypothesis. OH : u > 5.8 OH: M 2 5.8 OH: u # 5.8 OH: us 5.8 State the alternative hypothesis. OH: M = 5.8 OH: u # 5.8 OH_: H = 5.8 OH : H = 5.8 Part (b) State the p-value. (Round your answer to four decimal places.) Part (c) State alpha. (Enter an exact number as an integer, fraction, or decimal.) Part (d) What is your decision? O reject the null hypothesis O do not reject the null hypothesis Part (e) Write a conclusion O There is sufficient evidence to conclude that the mean number of visits of women with their doctor is more than 5.8. O There is not sufficient evidence to conclude that the mean number of visits of women with their doctor is more than 5.8.Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your answers to two decimal places.) 95% C.I.The mean age of graduate students at a University is at most 31 years with a standard deviation of two years. A random sample of 15 graduate students is taken. The sample mean is 32 years and the sample standard deviation is three years. Are the data significant at the 1% level? The p-value is 0.0264. State the null and alternative hypotheses. OH: us 31 H_ : u # 31 OH : M = 31 H_: u # 31 OH : M > 31 H:us 31 OH: M = 31 He: u > 31 OH : us 31 H_: u > 31 Interpret the p-value. O The p-value is 0.0264, so the data are significant at the 1% level. O The p-value is 0.0264, so the data are not significant at the 1% level