(1)The file 'MeatSelenium.csv' contains the selenium levels (mcg/100g) of a sample of 144 portions of beef raised in a particular region. The selenium levels are in the variable 'selen'. Let denote the average selenium level (mcg/100g) of all beef raised in this region. The minimum recommended daily intake for adults is 55 mcg. You will test whether a 100g serving of this meat exceeds the minimum recommended daily intake for adults. Use = 0.05.

(a)Always begin data analysis with an appropriate plot of the data. Start with a boxplot of the beef portion selenium levels. Include the plot here. Comment on what you see.

Answer:

(b)It's also a good idea to produce summary statistics of your data. Calculate the sample mean and sample variance for each gender. Include the output here.

(c)Now for the hypothesis test - what are the null and alternative hypotheses?

(d)Which test will you use, the t-test or z-test? What are the assumptions behind the test? Are they satisfied?

(e)Run the test and paste the output here.

(f)What conclusion do you reach? State the reasoning behind your conclusion and interpret your conclusion.

(g)Calculate a 95% confidence interval for = denote the average selenium level (mcg/100g) of all beef raised in this region. Interpret the confidence interval - how does it elaborate upon the conclusion from the hypothesis test above?

Data file:

type selen NRB 44.33 NRB 76.86 NRB 4.45 NRB 55.01 NRB 58.21 NRB 74.72 NRB 11.84 NRB 139.09 NRB 69.01 NRB 94.61 NRB 48.35 NRB 37.65 NRB 66.36 NRB 72.48 NRB 87.09 NRB 26.34 NRB 71.24 NRB 90.38 NRB 50.86 RRB 11.23 RRB 29.63 RRB 20.42 RRB 10.12 RRB 39.91 RRB 32.66 RRB 38.38 RRB 36.21 RRB 16.39 RRB 27.44 RRB 17.29 RRB 56.2 RRB 28.94 RRB 20.11 RRB 25.35 RRB 21.77 RRB 31.62 RRB 32.63 RRB 30.31 RRB 46.16 RRB 56.61 RRB 24.47 RRB 29.39 RRB 40.71 RRB 15.82 RRB 27.74 RRB 22.35 RRB 34.78 RRB 35.09 RRB 32.6 RRB 37.03 RRB 27 RRB 44.2 RRB 13.09 RRB 33.03 RRB 9.69 RRB 32.45 RRB 37.38 RRB 34.91 RRB 27.99 RRB 22.36 RRB 22.68 RRB 26.52 RRB 46.01 RRB 38.04 RRB 30.88 RRB 30.04 RRB 25.91 RRB 18.54 RRB 18.52 RRB 25.51 RRB 27.8 RRB 19.49 SQU 37.42 SQU 56.46 SQU 51.91 SQU 62.73 SQU 4.55 SQU 39.17 SQU 38.44 SQU 40.92 SQU 58.93 SQU 61.88 SQU 49.54 SQU 64.35 SQU 82.49 SQU 38.54 SQU 39.53 SQU 68.99 SQU 27.97 SQU 37.57 SQU 25.71 SQU 23.97 SQU 13.82 SQU 42.21 SQU 35.88 SQU 10.54 SQU 41.89 SQU 23.94 SQU 49.81 SQU 30.71 SQU 50 SQU 87.5 VEN 26.72 VEN 28.58 VEN 29.71 VEN 26.95 VEN 10.97 VEN 21.97 VEN 14.35 VEN 32.21 VEN 19.19 VEN 30.92 VEN 10.42 VEN 35.49 VEN 36.84 VEN 25.03 VEN 33.59 VEN 33.74 VEN 18.02 VEN 22.27 VEN 26.1 VEN 20.89 VEN 29.44 VEN 31.5 VEN 27.36 VEN 21.33 VEN 14.86 VEN 16.47 VEN 25.19 VEN 37.45 VEN 45.08 VEN 25.22 VEN 22.11 VEN 33.01 VEN 31.2 VEN 26.5 VEN 32.77 VEN 8.7 VEN 25.9 VEN 29.8 VEN 37.63 VEN 21.69 VEN 21.49 VEN 18.11