Can you please answer this question 1 and all of the sub problems and show all of the steps to the solution No SIM11:15 AM46% 4QUESTION 1The health of employees is measured periodically by weighing them. A random sample of 54 employees has a meanweight of 170 pounds with a standard deviation of 121.2 pounds. Test the claim that the mean weigh for all suchemployees is less than 200 pounds.HypothesisHo:На:p-valueConclusionb. Find a 95% Confidence IntervalConfidence Interval.Conclusion.

a) Null hypothesis: The average weight has gone down. H0 : μ = 200. Alternative hypothesis: Ha :μ < 200 Test statistic: The test statistic for hypothesis test for mean is given by: t=x¯-μ0sn=170-200121.254=-1.8204 Here, sample size is 54. Thus, the degrees of freedom for the test is 53(=54-1). Therefore, the df value is 53. Computation of P-value: The P-value of t-distribution at 53 degrees of freedom can be obtained using the excel formula “=T.DIST (-1.8204, 53)”. The p-value is 0.0372. Decision rule: If p-value ≤ α, then reject the null hypothesis. Otherwise, fail to reject the null hypothesis. Assume the level of significance is 0.05 Conclusion: The P-value is 0.0372 and the level of significance is 0.05. Here, P-value is less than the level of significance. Hence, the null hypothesis is rejected. Conclusion: There is sufficient evidence to conclude that the mean weight is less than 200. b) Since the population standard deviation is unknown, t distribution can be used for the computation of confidence interval. Thus, sample mean = 170. Sample standard deviation, s is 121.2. The sample size, n is 54. The degrees of freedom is 54-1 =53. From the EXCEL, using the formula, =T.INV.2T(0.05,53), the critical value is 2.0057 The margin of error is calculated as follows: Margin of error = t×(s/√n) = 2.0057×(121.2/√54) = 33.0805 The 95% confidence interval is given by: CI = point estimate ±Margin of error = 170 ± 33.0805 = (136.9195, 203.0805) That is, the 95% confidence interval contains 200. Therefore, there is enough evidence to conclude that mean weight is 200.