Hi. Can I please get help with these two problems from my statistics homework. I am a bit confused and have been struggling in this class a lot, so it would be helpful if you could provide step by step guidance on how to do these. We use r studios to do our assignments. For problem through, I computed the code in r studios and it computed a box plot and a histogram, but it will not let me upload it here.

Problem 2:

Statistics can help decide the authorship of literary works.Sonnets by a certain Elizabethan poet are known to contain an average of $\mu=8.9$ new words (words not used in the poet's other works). The standard deviation of the number of new words is $S= 2.5$.Now a manuscript with 6 new sonnets has come to light, and scholars are debating whether it is the poet's work.The new sonnets contain an average of $\bar{x}=10.2$ words not used in the poet's known works.We expect poems by another author to contain more new words, so to see if we have evidence that the new sonnets are not by our poet we test the following hypotheses:

* Hypotheses:Null Hypothesis: $H_{0}: \mu=8.9$ versus $H_{a}: \mu > 8.9$.

Perform the hypothesis test using a T test statistic and its P-value.Give a complete conclusion that addresses the authorship of these new poems?

ANSWER:

* Test Statistic:$T=$

* P-Value:

* Conclusion:

*(part 1)

*(part 2)

*(part 3)

*(part 4)

Problem 3:

A manufacturer of a diet cola test a new formulation by storing in a room at high temperature for a month to simulate the conditions of normal storage for 6 months.The goal is to determine if the sweetness changes after storage.Sweetness was determined by trained tasters before and after storage.The change is defined as before minus after, and are given in the code block below.

```{r}

sweetness<-c(2.0,.4,.7,2.0,-.4,2.2,-1.3,1.2,1.1,2.3)

length(sweetness)

summary(sweetness)

sd(sweetness)

boxplot(sweetness)

hist(sweetness)

t.test(sweetness,mu=0)

wilcox.test(sweetness,mu=0)

```

[1] 10 Min. 1st Qu. Median Mean 3rd Qu. Max. -1.300 0.475 1.150 1.020 2.000 2.300 [1] 1.196105 One Sample t-test data: sweetness t = 2.6967, df = 9, p-value = 0.02453 alternative hypothesis: true mean is not equal to 0 95 percent confidence interval: 0.1643582 1.8756418 sample estimates: mean of x 1.02 cannot compute exact p-value with ties Wilcoxon signed rank test with continuity correction data: sweetness V = 47.5, p-value = 0.04657 alternative hypothesis: true location is not equal to 0 

\clearpage

Part a:Use a T test to determine if there is evidence the population mean sweetness change differs from zero.

* Hypotheses: $H_{0}: \mu=0$ vs $H_{a}: \mu eq 0$

* Test Statistic:

* P-value:

* Conclusion:

Part b. Use a 95 percent confidence interval to determine if there is evidence the cola sweetness changes after storage.If yes, how does it change?Give the confidence interval and a full conclusion based on the confidence interval.

Answer:

* c.Is is appropriate to use a T method for these data?Why or why not?

Answer c:

Part d:Use Wilcoxon test to determine if there is evidence the population median sweetness change differs from zero.

* Hypotheses: $H_{0}: median = 0$ vs $H_{a}: median eq 0$

* Test Statistic:

* P-value:

* Conclusion: