Question

In: Statistics and Probability

The manufacturer of a certain brand of cigarettes states that the nicotine content in their cigarettes...

The manufacturer of a certain brand of cigarettes states that the nicotine content in their cigarettes is 18.2mg with a standard deviation of 1.15mg. An independent testing agency
examined a random sample cigarettes (sample below). At a 5% level of significance, is there evidence for the testing agency to conclude that the mean nicotine level to be other than the company states?
Cigarette Nicotine Level (mg)

19.51 17.34 19.58 18.31 18.98 19.02 18.63 18.4 18.32 17.74 18.82 17.92 17.77

18.54 17.93 17.01 17.23 19.25 17.09 17.32 17.97 19.29 18.77 19.34 18.57 17.33

19.29 17.8 17.12 17.74 17.3 19.45 18.76 18.81 17.78 17.21 17.49 18.9 17.73

19.42 19.25 18.63 17.76 19.16 18.36 19.6 17.19 17.63 18.83 18.34 18.06 17.44

17.82 17.51 18.17 19.3 18.14 17.11 18.74 19.22 18.55 18.92 19.19 19.17 18.05

18.52 17.72 19.02 18.21 18.97 17.17 18.61 18.43 18.44 19.12 19.04 18.87 18.13

18.14 19.09 19.1 18.47 18.31 17.42 19.17 19.56 18.43 18.13 18.42 17.38 17.98

18.22 19.49 17.9 18.17 18.61 17.82 19.55 18.91 19.39 17.73 18.51 17.54 19.08

19.4 18.46 18.13 17.92 17.27 18.54 19.34 18.05 17.26 17.59 19.47 18.1 18.14

19.1 18.42 17 17.17 19.53 17.93 17.9 18.62 17.53 18.19 17.53 17.59 19.36

17.62 17.73 17.85 18.58 18.21 18.85 18.1 17.35 18.62 19.02 17.87 18.76 18.1

18.48 18.07 18.62 18.16 19.16 18.56 18.35 18 17.86 17.39 19.49 19.37 17.41

19.03 19.28 17.17 18.58 17.54 17.77 17.78 18.4 17.36 17.09 18.46 18.43 18.65

17.1 17.48 17.74 17.34 17.08 17.8 18.04 18.68 17.52 19.59 19.21 17.65 18.49

19.13 18.31 17.26 17.33 19.45 18.62 19.46 19.22 18.06 17.69 18.55 19.2 17.47

18.22 19.19 18.96 18.71 17.56 19.6 17.4 19.24 19.16 17.04 17.65 17.9 17.57

19.36 19.18 17.91 18.8 17.47 18.61 17.17 19.05 17.55 19.1 18.56 17.95 18.86

18.45 18.24 19.57 17.1 18.03 18.09 19.34 19.51 18.93 18.5 19.08 18.7 18.58

18.31 19.6 18.09 17.26 17.43 18.08 18.28 19.39 17.79 18.66 18.53 18.95 17.67

18.19 18.66 19.17 18.5 18.35 19.13 19.48 19.11 17.84 18.83 17.51 18.26 18.91

17.74 17.1 18.47 17.75 17.01 17.81 19.28 18 18.85 17.65 17.68 19.34 17.58

BLANK #1: Is this a question involving mean or proportion? ***ANSWER "MEAN" OR "PROPORTION" (WITHOUT THE QUOTATION MARKS)***

BLANK #2: Which type of distribution should be used to calculate the probability for this question? ***ANSWER "NORMAL", "T", OR "BINOMIAL" (WITHOUT THE QUOTATION MARKS)***

BLANK #3: Which of the following options are the appropriate hypotheses for this question: ***ANSWER WITH THE CORRECT LETTER, WITHOUT ANY QUOTATION MARKS OR BRACKETS***

A) H0: μ = 18.2mg H1: μ > 18.2mg

B) H0: μ = 18.2mg H1: μ < 18.2mg

C) H0: μ = 18.2mg H1: μ ≠ 18.2mg

D) H0: p = 18.2mg H1: p > 18.2mg

E) H0: p = 18.2mg H1: p < 18.2mg

F) H0: p = 18.2mg H1: p ≠ 18.2mg

BLANK #4: What is the p-value of this sample? ***ANSWER TO 4 DECIMALS, BE SURE TO INCLUDE LEADING ZERO, EXAMPLE "0.1234"...NOT ".1234"***

BLANK#5: Based on this sample, at a 5% level of significance, is there evidence for the testing agency to conclude that the mean nicotine level to be other than the company states? ***ANSWER "YES" OR "NO" (WITHOUT THE QUOTATION MARKS)***

Solutions

Expert Solution

Hypothesis test:

Mean

Normal

C) H₀: μ = 18.2mg H₁: μ ≠ 18.2mg

p-value = 0.0618

Please upvote if you have liked my answer, would be of great help. Thank you.

orchestra answered 1 year ago

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