Question

) A sample of historical 120 months' river flow is collected and the following is determined: the sample mean is 430 mls, sample standard deviation is 28 m/s. Determine a confidence interval of 95%. In the class of 300 children surveyed, the sample mean weight was 11.3 kg and the standard deviation was 1.8 kg. Find the 99% confidence interval for this data. 2) In a shop, apples are packed in 2 kg bags. A customer suspects the bags may not contain 2 kg. A sample of 40 bags produces a mean of 1.7 kg and a standard deviation of 0,9 kg. Is there enough evidence to conclude that the bags do not contain 2 kg as stated, at 3) nd the 95% confidence interval of the true mean. What will be the -0.05? Also, fi o 0.01? case at

Answer 1

Solution-1: Sample size n 120 Sample Sample Standard Deviation = S = 28 Degrees of freedom =df = n-1 120-1-119 For 95% confidence interval, α 1-0.95 0.05 a/2 0.05/2 0.025 From t-distribution table, the value of t having an area of (α/2 = 0.025) in its upper tail and for (df = 119) is given by mean-x-430 t0.025 1.980 Margin of Error MoE to.o25 28 MoE1.980 V120 MoE 5.061 95% confidence interval: Lower Limit of 95% confidence interval-430-5.061 424.939 Upper Limit of 95% confidence interval 430 + 5.061-435.061 Solution-2: Sample size-n- 300 Sample mean - 11.3 Sample Standard Deviation S 1.8 Degrees of freedom-df-n-1 3001 For 99% confidence interval, α 1-0.99-0.01 299

a/2 0.01/2 0.005 From t-distribution table, the value of t having an area of (a/2 0.005) in its upper tail and for (df - 299) is given by 0.005 = 2.592 Margin of Error MoE to.oos 0,005 × S 1.8 MoE = 2.592 × 300 MoE0.269 99% confidence interval: Lower Limit of 99% confidence interval 11.3-0.269 Upper Limit of 99% confidence interval-11.3 + 0.269 11.031 11.569 Solution-3: Sample size n- 40 Sample mean = 1.7 Sample Standard Deviation S 0.9 Test Statistic: (0.9/V40)

α 0.01 As calculated above, P-value 0.0414 Since p-value> a, we fail to reject the null hypothesis Hence, at α = 0.01, there is not sufficient evidence to conclude that the bags do not contain 2 kg as stated.