Question

# A random sample of 22 STAT 250 students was collected and the file size of Data...

A random sample of 22 STAT 250 students was collected and the file size of Data Analysis 2 was recorded. The data was measured in megabytes. The instructors of the course claim that the file size will be different from 5 megabytes. Consider the population of all file sizes to be right skewed. Using a= 0.01, is there sufficient evidence to conclude that the mean file size of Data Analysis 2 is different from 5 megabytes? Conduct a full hypothesis test by following the steps below. Enter an answer for each of these steps in your document.

a) Define the population parameter in one sentence.

b) State the null and alternative hypotheses using correct notation.

c) State the significance level for this problem.

d) Create a histogram and a box plot of the sample data and copy these into your document. (Sample data is 7.72 4.49 8.17 5.51 9.09 7.41 6.31 2.04 5.5 3.85 4.43 3.97 0.89 5.41 4.49 4.88 2.21 1.97 6.82 9.8 5.96 7.65)

e) Use the graphs created in part (d) to check the conditions that allow you to calculate the test statistic in one to two sentences.

f) No matter your results in part (d & e), calculate the test statistic “by-hand.” Show the work necessary to obtain the value by typing your work and provide the resulting test statistic. Do not round during the calculation. Then, round the test statistic to two decimal places after you complete the calculation.

g) Use StatCrunch (Stat  T Stats  One Sample  with Data) to verify your test statistic. Copy and paste this box into your document.

h) State the p-value using the output provided in part (g). Use four decimal places for the p- value. In addition, state the degrees of freedom.

i) State whether you reject or do not reject the null hypothesis and the reason for your decision in one sentence.

j) State your conclusion in context of the problem (i.e. interpret your results and/or answer the question being posed) in one or two complete sentences.

k) Construct a 99% confidence interval using StatCrunch. Copy the output into your document as your answer.

l) Explain the connection between the confidence interval and the hypothesis test in this problem (discuss this in relation to the decision made from your hypothesis test and connect it to the confidence interval you constructed in part (k)). Answer this question in one to two sentences.

Solution-A:

population parameter is mean  file size

Solution-B:

null hypothesis

Ho:

Alternative hypothesis

Ha:

Solution-c:

alpha=0.01

Solution-d:

Select the data in excel.

Insert>chart

From histogram we see data follows normal distribution

In excel

insert>boxplot

From bopxlot we see

minimum=0.89

Q1=3.94

Q2=5.455

Q3=7.47

maximum=9.8

No outliers found

Solution-e:
From histogram we could see sample data follows normal distribution.

Solution-f:

t statistic is

t=xbar-mu/(s/sqrt(n)

where xbar=smaple mean=5.389545

s=sample stdev= 2.382451

mu=population eman=5

n=sample size=22

t=(5.389545-5)/(2.382451/sqrt(22))

t=0.77

test statistic,t=0.77

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