A quality control specialist at a pencil manufacturer pulls a random sample of 45 pencils from the assembly line. The pencils have a mean length of 17.9 cm. Given that the population standard deviation is 0.25 cm, find the p-value you would use to test the claim that the population mean of
pencils produced in that factory have a mean length equal to 18.0 cm.

The p-value you would use to test the claim

p -value = 0.007

Step-by-step explanation:

Step(i):-

Given random sample size 'n' = 45

Mean of the Population = 18.0 c.m

Standard deviation of the Population(S.D) = 0.25 c.m

Mean of the sample = 17.9 c.m

Null hypothesis :-

               H₀ : μ = 18.0 c.m

Alternative Hypothesis:

             H₁ :  μ ≠ 18.0 c.m

Test statistic

|Z| = |-2.688|

|Z| = 2.688≅ 2.7

Step(ii):-

P -value :-

The z-test statistic value = 2.7

P( Z>2.7) = 1- P(Z< 2.7)

                  = 1- ( 0.5+ A(2.7))

                  = 0.5 - A(2.7)

                  = 0.5 - 0.4965

                 = 0.0035

P( Z>2.688)= 0.0035

Given data is two tailed test

2 X P( Z>2.688) = 2 X 0.035 = 0.007

P-value = 0.007

we will choose level of significance ∝=0.05

P -value < 0.05

H₀ is rejected

Alternative Hypothesis is accepted

Final -

The population mean of  pencils produced in that factory have a mean length is not equal to 18.0 cm.    

see below

step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

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5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.  

whats the