Normal Quantile Plot - Mean and sample Standard Deviation - Statistics Scenario Assessment Answer

Scenario

Nick is a third year food technology student. His grandfather George owns a vineyard. Nick remembers visiting his grandfather every school holiday and helping him in his vineyard. Lately George often complains about the grapes ripening too early and that the taste of their homemade wine is getting sweeter and less acidic. According to George, the reason for all of these changes is climate warming and higher temperatures in this region.
Nick decides to test George’s claim. He randomly selects vineyards from a surrounding large region, where traditionally people harvested the same varieties of grapes as his grandfather. According to George, up until 10 years ago he always harvested his grapes on the second Saturday of February. For each vineyard, Nick records the date when the grapes were harvested this year. Using this information he then records how many days earlier or later is this date compared to the second Saturday of February. He also records measurements of the acidity of the wines produced from these grapes.

The Analysis Tasks
The questions you need to answer in your assignment submission are given below. Please make sure your assignment submission is converted to pdf format.
1. This question is about describing the variability of the dates of early or late harvest this year.
(a)  i. Calculate the sample mean and sample standard deviation of your sample of DD measurements.
      ii. What is your sample size n?
(b) Produce a boxplot of your sample of DD measurements. Include this boxplot in your submitted assignment, properly labelled.

(c) Summarize the key features of your boxplot from Part 1b, commenting on central location, spread, shape and (any) outliers.

(d) Produce a normal quantile plot of your sample of DD measurements. Include this plot in your submitted assignment, properly labelled.
(e) By referring to the normal quantile plot obtained in Part 1d briefly discuss if the DD measurements are approximately normally distributed.
2.  In this question you are estimating how close to the second Saturday in February were harvests this year.
(a) Produce a 95% confidence interval for the true mean DD (in days) this year, for the region where George has a vineyard. For this question you may assume that it is appropriate to use a t-distribution. Include your working. Show all the required steps to calculate this interval.
You can give RStudio command/output.
(b)  Does this confidence interval in Part 2a include the value of 0?
(c)  Explain in simple language what this 95% confidence interval in Part 2a means and how can we relate whether or not this confidence interval includes the value of 0 and George’s claim about the warming climate.
3.  Let μ be the true mean pH acidity level this year for wines in this region. Nick wants to compare the current mean acidity level with the mean from ten years ago. The known mean acidity level from ten years ago corresponded to a pH of 3.2.
(a) Produce a normal quantile plot of your sample of WA measurements. Include this plot in your submitted assignment, properly labelled.
(b) By referring to the normal quantile plot obtained in Part 3a briefly discuss if the WA measurements are approximately normally distributed.

4(c)Test the hypothesis that μ is equal to 3.2. You must summarize all steps: state the null (H0) and alternative hypotheses (Ha) relevant to the research objectives stated in this scenario; state a suitable test statistic and its observed value; the sampling distribution for this statistic; a P-value; your summary of significance and conclusion in plain language. Include your working. For parts involving calculations, show how you arrived at your answer. You can give RStudio commands/output. But try to keep your
solutions brief and concise.
(d) Some assumptions need to be made for the sampling distribution of the test statistic (as given in Part 3c) to be valid. State these assumptions.
(e) Discuss whether the assumptions from Part 3d are satisfied.
4.  George is concerned that the Maria grapes are losing crispiness. Maria wine is changing its flavour as the taste is getting less acidic. Traditionally both Jessica and Maria wines were of very similar acidity. Nick decides to examine the relationship between the grape type (JM measurements) and the wine acidity (WA measurements) in his samples.
(a) Produce a comparative boxplot for wine acidity against grape type. Include this plot in your submitted assignment, properly labelled.
(b) Describe any di↵erences or similarities in the distribution of wine acidity for the di↵erent grape types using your comparative boxplot from Part 4a. Comment on the central location, spread, shape and (any) outliers.

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