Question

According to data from the Tobacco Institute Testing Laboratory, a certain brand of cigarette contains an average of 1.4 milligrams of nicotine. An advocacy group questions this figure, and commissions an independent test to see if the the mean nicotine content is higher than the industry laboratory claims.
The test involved randomly selecting n=15n=15 cigarettes, measuring the nicotine content (in milligrams) of each cigarette. The data is given below.

1.7,1.6,1.8,2.0,1.4,1.4,1.9,1.6,1.3,1.5,1.2,1.4,1.7,1.2,1.51.7,1.6,1.8,2.0,1.4,1.4,1.9,1.6,1.3,1.5,1.2,1.4,1.7,1.2,1.5

(a) Do the data follow an approximately Normal distribution? Use alpha = 0.05.  ? yes no

(b) Determine the PP-value for this Normality test, to three decimal places.
P=P=

(c) Choose the correct statistical hypotheses.
A. H0:X¯¯¯¯>1.4,HA:X¯¯¯¯<1.4H0:X¯>1.4,HA:X¯<1.4
B. H0:X¯¯¯¯=1.4,HA:X¯¯¯¯<1.4H0:X¯=1.4,HA:X¯<1.4
C. H0:μ>1.4,HA:μ<1.4H0:μ>1.4,HA:μ<1.4
D. H0:μ=1.4HA:μ>1.4H0:μ=1.4HA:μ>1.4
E. H0:μ=1.4,HA:μ≠1.4H0:μ=1.4,HA:μ≠1.4
F. H0:X¯¯¯¯=1.4,HA:X¯¯¯¯≠1.4H0:X¯=1.4,HA:X¯≠1.4


(d) Determine the value of the test statistic for this test, use two decimals in your answer.
Test Statistic =

(e Determine the PP-value for this test, to three decimal places.
P=P=

(f) Based on the above calculations, we should  ? reject not reject  the null hypothesis. Use alpha = 0.05

Answer 1

To solve Part a & b.

The test statistic is obtained as shown below:
Instruction of MegaStat to obtain the test statistic is given as:
1.In EXCEL, Select Add-Ins > Mega Stat > Hypothesis Tests.
2.Choose Mean Vs Hypothesized Value.
3.Choose Data Input.
4.Enter A2:A16 Under Input Range.
5.Enter 0 Under Hypothesized mean.
6.Check t-test, enter Confidence level as 95.0.
7.Choose not equal (or greater than, less than) in alternative.
8.Click OK.
Follow the above instructions to obtain the MegaStat output:

To solve Part c, d, e, f.

Given that,
population mean(u)=1.4
provided sample data ( 1.7,1.6,1.8,2.0,1.4,1.4,1.9,1.6,1.3,1.5,1.2,1.4,1.7,1.2,1.5 )
sample mean, x =1.5467
standard deviation, s =0.2416
number (n)=15
null, Ho: μ=1.4
alternate, H1: μ>1.4
level of significance, alpha = 0.05
from standard normal table,right tailed t alpha/2 =1.761
since our test is right-tailed
reject Ho, if to > 1.761
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =1.5467-1.4/(0.2416/sqrt(15))
to =2.3517
| to | =2.3517
critical value
the value of |t alpha| with n-1 = 14 d.f is 1.761
we got |to| =2.3517 & | t alpha | =1.761
make decision
hence value of | to | > | t alpha| and here we reject Ho
p-value :right tail - Ha : ( p > 2.3517 ) = 0.01693
hence value of p0.05 > 0.01693,here we reject Ho
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(a) From the MegaStat output, all the data points are very close to each other. It can be concluded that the data follows an approximately normal distribution. If the data points are far away from each other, it can be concluded that the data does not follow normal diatribution.
(b) The P-value for the normality test is 0.716
(c) D. H0:μ = 1.4; Ha:μ>1.4
(d) test statistic: 2.3517
(e) p-value: 0.01693
(f) decision: reject Ho