Sunspots have been observed for many centuries Records of su

Sunspots have been observed for many centuries. Records of sunspots from ancient Persian and Chinese astronomers go back thousands of years. Some archaeologists think sunspot activity may somehow be related to prolonged periods of drought in the southwestern United States. Let x be a random variable representing the average number of sunspots observed in a four-week period. A random sample of 40 such periods from Spanish colonial times gave the data which can be found on Canvas under Instructions for Data Analysis #3. (Reference: M. Waldmeir, Sun Spot Activity, International Astronomical Union Bulletin). It is thought that for thousands of years, the mean number of sunspots per 4-week period was about 41. Sunspot activity above this level may be linked to gradual climate change. Do the data indicate that the mean sunspot activity during the Spanish Colonial period was higher than 41? Use a significance level of 0.05. Use the provided R code to obtain descriptive statistics, graphical displays and p-values. Show all work. Work must be neat and readable.

a. Include a plot of the data.

b. Is there visual evidence that the true mean is more than 41 sunspots per 4-week period during the Spanish colonial period? Explain. Must include context.

c. State the null and alternative hypothesis to answer the researcher’s question of interest.

d. Calculate the test statistic by hand and obtain a p-value by table. Show work.

e. Calculate the 95% Confidence Interval by hand. Show work.

f. Obtain a p-value from t-test and confidence interval using R. Copy the R output for the hypothesis test and confidence interval and paste it. Are your answers different than d and e?

g. Using the R output (from f) give a four part conclusion (shown in notes) and thoroughly answer the researchers question of interest. Must include context.

h. : Append R Code to the end

R code.

sun = read.csv(file.choose(), header= TRUE)

#Check Out first 6 lines Data
head(sun)

# Make a Boxplot
boxplot(sun$spots, main= \"Boxplot of Sunspots
duirng Spanish colonial times\", xlab = \"Mean number of sunspots
in a 4-week period\", horizontal = TRUE, col = \"blue\")

# Get Mean
mean(sun$spots)

# Get Satndard Deviation
sd(sun$spots)

#Get Sample Size
length(sun$spots)

# Perform t Test
t.test(sun$spots, mu=41, alternative = \"greater\")

# Calculate Confidence Interval
confidenceinterval=t.test(sun$spots, mu = 41)$conf.int
confidenceinterval

The data

Solution