plz include full working outs and excel formulas
She measured plant growth in cm with an uncertainty of +/-0.5 cm. The data is: BATCH 1: 4.5, 5.9, 4.3, 6.6, 6. 1, 5.5, 5.8, 5. 4, 5.2, 4.9, 5. 7, 5.3, 6.0, 4.9, 6.2, BATCH 2: 6.0, 5.5, 5.2, 5.0, 4.8, 4.6, 4.6, 5.0, 5.3, 4.8, 5.6, 5.8, 5.4, 4.7, 5.3 PART A: Standard Deviation (4 Marks) 1. Calculate the mean growth of plants in Batch 1 and Batch 2. 2. Calculate the standard deviation of the mean growth of plants in Batch 1 and Batch 2. Note, she included all of her plants which is the entire population, so you will need to use STDEV. P in excel. 3. Draw a table to summarise your results. Do not forget to include units. PART B: Confidence Interval (8 Marks) Batch 2 is used to estimate the population mean for all plants using the Normal Distribution. 1. Identify the following parameters for Batch 2: 3 a. H = b. O= C. n= 2. Construct a 90% confidence interval for the population mean plant growth. 3. Use a complete sentence to explain what the confidence interval means. Template: "It is estimated with _% confidence that the true population mean (include the context of the problem) is between_ and _ (include appropriate units)." PART C: Graphing (3 Marks) 1. Use Excel to draw an appropriate graph to display the means of Batch 1 and Batch 2. 2. Add 'The Standard Error' as error bars. See the separate instruction sheet if you need some help. 3. Add a title and appropriate labels to your graph and copy it to your report. 3 PART D: Hypothesis T-Test (10 Marks) Use excel to carry out a t-test for the growth of plants in Batch 1 and Batch 2 using the following null hypothesis H.= The average growth for Batch 1 is not more than the average growth for Batch 2. 1. Write a mathematical statement to represent the null hypothesis. 2. State what the alternative hypothesis is, in words and a mathematical statement. 2 3. Calculate the P-Value, ensure you include your excel formula and results. 2 Use the T. TEST function explained below. Check the last page on what type should be used. EXCEL =T.TEST(array1,array2, tails,type) Returns the probability associated with a Student's t-Test. array1 is the first data set array2 is the second data set tails specifies the number of distribution tails to return, one-tailed distribution = 1; two-tailed distribution = 2. type is the kind of t-test; paired = 1, two-sample equal variance (homoscedastic) = 2, two-sample unequal variance = 3. Change your EXCEL output for the T. TEST function result into a decimal number so it can be easily compared with P If P > 5% then the two sets are the same (i.e. fail to reject the null hypothesis as P is greater). If P
