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Owner: jev2014
Created: Mar 25, 2018
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MTH 245 Stats Lab 8 - J. Vandeloecht
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1.     Is the population standard deviation,, known?

 The standard deviation is not known.

 

2.       Are either of the requirements of (a) normality or (b) sample size > 30 met by the data set?  To support your normality assessment, create (and attach to your report) a histogram, boxplot, and QQ plot.

While the same size is not greater than 30, the requirements for normality are met as shown on the box plot and QQ plot. The histogram does not necessarily show a normal distribution and I attribute that to the small sample size.

3.       Considering your answers to questions 1 and 2, what hypothesis test should you use (t test, z test, or bootstrapping?)

Since the standard deviation is not known and the sample is normally distributed we will conduct a t test.

4.       Is this a one-tailed or two-tailed test?

This is a one-tailed test. (left tailed)

5.       Write the claim in sentence form.

Students who watch at least 3 hours of television a night will read less than 52 words per minute. 

6.       Write the claim in mathematical form. 

µ < 52

7.       Which hypothesis does the claim represent? 

The claim represents the alternative hypothesis.

8.       Write the alternative and null hypotheses using correct notation.

a.       H1 :  µ  = 52

b.       H0 :  µ < 52

9.     What is your significance level, ?

      a = 0.05   

10.   Based on your answers to questions 3, 8, and 9, what is/are the critical value(s) (t or z)?

 t = -3.813

11.   From your sample data, what are the values for each of the following?  

a.       mean = 45.2667

b.       degrees of freedom =  N = 15 / N – 1 = 14   DF = 14

c.       standard error =   1.766

d.       test value (t or z)  = -1.7613

e.       p-value= .001

12.   Based on the results of the hypothesis test, do you reject the null or fail to reject the null?  Explain your decision.

            Based on the results I would reject the null hypothesis because the test statistic of t =                      -3.813 falls within the critical region.    

13.   Using proper notation in reference to the claim, write your conclusion and results as if they were going to be reported in a manuscript.

          There is enough evidence to reject   H1 :  µ  = 52 when a student watches television                             for at least 3 hours a night since t = -3.813 and falls in the critical region.

 

 

 

Result 1: MTH 245 Stats Lab 8 - Summary Stats - J. Vandeloecht   [Info]
Summary statistics:
ColumnnMeanVarianceStd. dev.Std. err.MedianRangeMinMaxQ1Q3
Reading1545.26666746.7809526.83966031.7659927462334573851

Result 2: MTH 245 Stats Lab 8 - Histogram - J. Vandeloecht   [Info]
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Result 3: MTH 245 Stats Lab 8 - Boxplot - J. Vandeloecht   [Info]
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Result 4: MTH 245 Stats Lab 8 - QQ Plot - J. Vandeloecht   [Info]
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Result 5: MTH 245 Stats Lab 8 - One sample T hypothesis test - J. Vandeloecht   [Info]
One sample T hypothesis test:
μ : Mean of variable
H0 : μ = 52
HA : μ < 52

Hypothesis test results:
VariableSample MeanStd. Err.DFT-StatP-value
Reading45.2666671.765992714-3.81277530.001

Result 6: MTH 245 Stats Lab 8 - T Calculator - J. Vandeloecht   [Info]
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Data set 1. MTH 245 Stats Lab 8 - Data Set 1 - J. Vandeloecht   [Info]
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By remetzger
Mar 25, 2018

Great job, Jed! You reversed part 10 and 11(d), and state your conclusion in a way that will be understood by anyone: "There is sufficient evidence to support the claim that excessive television watching decreases reading ability." Really nice job, here. You get it.

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