A confectionery factory uses imported cocoa beans to make small chocolate bars. Randomly chosen chocolate bars...

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A confectionery factory uses imported cocoa beans to make small chocolate bars. Randomly chosen chocolate bars are tasted and given a taste quality score; a numerical value ranging from 0 to 10. Based on past data the taste quality score is, on average, 9.25 for chocolate bars made from the current source of cocoa beans. It is known that cocoa beans from different sources can affect the taste quality of the chocolate bars. Management has been advised that sales would increase if the current mean taste quality score can be increased by at least 0.3, whereas sales would decrease if the mean taste quality score drops by 0.5 or more, assuming all other factors remain fixed. Any change in the mean taste quality score of between these two values would be of no consequence with respect to sales. A study is conducted by the quality control team to determine what effect a new source of cocoa beans will have on the current taste quality mean score of 9.25 for the purpose of identifying a sales effect. Some possible outcomes of the study using the new source of cocoa beans are: se(x) P-value Case 1 Case 2 Case 3 Case 4 Case 5 8.44 9.12 8.9 9.92 8.97 X 0.1380 0.1120 0.4700 0.0690 0.0390 0.0000 0.5938 0.4190 0.0000 0.0000 (8.16, 8.72) (8.9, 9.34) (7.96, 9.84) (9.78, 10.06) (8.89, 9.05) Note: The hypotheses associated with the quoted P-values are: Ho: The underlying mean taste quality score is 9.25. H₁: The underlying mean taste quality score is not 9.25. a) What is the hypothesised value? 9.25 b) Select the correct options to complete the sentence about Case 4: The estimated mean in Case 4 (x = 9.92) is 9.74 95% CI (2d.p.) standard errors above c) Which case(s) demonstrates, at the 5% level of significance, that the observed mean, X, is statistically different from the hypothesised value? Cases 1, 4 and 5 the hypothesised value. d) In which case(s) are we are able to claim that the underlying mean taste quality score using the new source of cocoa beans: - has practical significance Cases 1, 4 and 5 - does not have practical significance Cases 2 and 3 e) Select one case in which we have learned nothing useful about the underlying mean taste quality score using the new source of cocoa beans Case 1 f) Suppose the actual outcome for the study is: se(x) X 8.31 P-value Case 6 Select the correct option to complete the sentences interpreting this output: In this case the mean taste quality score when using the new source of cocoa beans is statistically significant (at the 5% level). 0.045 95% CI (8.02, 8.60) 0.0025 We are practical importance. With 95% confidence the underlying mean taste quality score when using the new cocoa source is estimated to be somewhere between 8.02 and * able to claim that the underlying mean taste quality score has 8.60 lower current cocoa source). Based on these results I would recommend using the current than 9.25 (the average from the A confectionery factory uses imported cocoa beans to make small chocolate bars. Randomly chosen chocolate bars are tasted and given a taste quality score; a numerical value ranging from 0 to 10. Based on past data the taste quality score is, on average, 9.25 for chocolate bars made from the current source of cocoa beans. It is known that cocoa beans from different sources can affect the taste quality of the chocolate bars. Management has been advised that sales would increase if the current mean taste quality score can be increased by at least 0.3, whereas sales would decrease if the mean taste quality score drops by 0.5 or more, assuming all other factors remain fixed. Any change in the mean taste quality score of between these two values would be of no consequence with respect to sales. A study is conducted by the quality control team to determine what effect a new source of cocoa beans will have on the current taste quality mean score of 9.25 for the purpose of identifying a sales effect. Some possible outcomes of the study using the new source of cocoa beans are: se(x) P-value Case 1 Case 2 Case 3 Case 4 Case 5 8.44 9.12 8.9 9.92 8.97 X 0.1380 0.1120 0.4700 0.0690 0.0390 0.0000 0.5938 0.4190 0.0000 0.0000 (8.16, 8.72) (8.9, 9.34) (7.96, 9.84) (9.78, 10.06) (8.89, 9.05) Note: The hypotheses associated with the quoted P-values are: Ho: The underlying mean taste quality score is 9.25. H₁: The underlying mean taste quality score is not 9.25. a) What is the hypothesised value? 9.25 b) Select the correct options to complete the sentence about Case 4: The estimated mean in Case 4 (x = 9.92) is 9.74 95% CI (2d.p.) standard errors above c) Which case(s) demonstrates, at the 5% level of significance, that the observed mean, X, is statistically different from the hypothesised value? Cases 1, 4 and 5 the hypothesised value. d) In which case(s) are we are able to claim that the underlying mean taste quality score using the new source of cocoa beans: - has practical significance Cases 1, 4 and 5 - does not have practical significance Cases 2 and 3 e) Select one case in which we have learned nothing useful about the underlying mean taste quality score using the new source of cocoa beans Case 1 f) Suppose the actual outcome for the study is: se(x) X 8.31 P-value Case 6 Select the correct option to complete the sentences interpreting this output: In this case the mean taste quality score when using the new source of cocoa beans is statistically significant (at the 5% level). 0.045 95% CI (8.02, 8.60) 0.0025 We are practical importance. With 95% confidence the underlying mean taste quality score when using the new cocoa source is estimated to be somewhere between 8.02 and * able to claim that the underlying mean taste quality score has 8.60 lower current cocoa source). Based on these results I would recommend using the current than 9.25 (the average from the