Question

Problem 1 Install the R package texmex and load the data sets winter and summer, which contain the measurements for Leeds, UK air pollutants in each season. a) Verify that winter and summer nitrogen dioxide concentration can reasonably be assumed to be normally distributed with presentation-quality plots. Paste them below. b) We wish to determine whether the variances of winter and summer nitrogen dioxide concentrations are equal at significance level 0.01. Write appropriate hypotheses. Use VarTest to conduct the test. c) How does VarTest conduct the test in part b? Explain the sampling distribution used, and explain how the observed test statistic was computed. d) Now test $H_0: \mu_{NO_2}^{(summer)} = \mu_{NO_2}^{(winter)}$ vs. $H_A: \mu_{NO_2}^{(summer)} \neq \mu_{NO_2}^{(winter)}$ at significance level 0.01. Determine whether you can assume the variances are equal or unequal based on your answer to part b). Just use an appropriate R function for this problem but report the output. Comment in the context of air quality during summer and winter.

          Problem 1
Install the R package texmex and load the data sets winter and summer, which contain the
measurements for Leeds, UK air pollutants in each season.
a)
Verify that winter and summer nitrogen dioxide concentration can reasonably be assumed to be normally
distributed with presentation-quality plots. Paste them below.
b)
We wish to determine whether the variances of winter and summer nitrogen dioxide concentrations are
equal at significance level 0.01. Write appropriate hypotheses. Use VarTest to conduct the test.
c)
How does VarTest conduct the test in part b? Explain the sampling distribution used, and explain how the
observed test statistic was computed.
d)
Now test $H_0: \mu_{NO_2}^{(summer)} = \mu_{NO_2}^{(winter)}$ vs. $H_A: \mu_{NO_2}^{(summer)} \neq \mu_{NO_2}^{(winter)}$ at significance level 0.01. Determine
whether you can assume the variances are equal or unequal based on your answer to part b). Just use an
appropriate R function for this problem but report the output. Comment in the context of air quality
during summer and winter.

Problem 1
Install the R package texmex and load the data sets winter and summer, which contain the
measurements for Leeds, UK air pollutants in each season.
a)
Verify that winter and summer nitrogen dioxide concentration can reasonably be assumed to be normally
distributed with presentation-quality plots. Paste them below.
b)
We wish to determine whether the variances of winter and summer nitrogen dioxide concentrations are
equal at significance level 0.01. Write appropriate hypotheses. Use VarTest to conduct the test.
c)
How does VarTest conduct the test in part b? Explain the sampling distribution used, and explain how the
observed test statistic was computed.
d)
Now test H0: μNO2^(summer) = μNO2^(winter) vs. HA: μNO2^(summer)≠μNO2^(winter) at significance level 0.01. Determine
whether you can assume the variances are equal or unequal based on your answer to part b). Just use an
appropriate R function for this problem but report the output. Comment in the context of air quality
during summer and winter.

Added by Jamie M.

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