Mary brought chocolate and vanilla cupcakes to school for her birthday. 21 students picked a vanilla cupcake and 7 students pick
2 answers:
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Answer:
The p-value you would use to test the claim
p -value = 0.007
Step-by-step explanation:
<u><em>Step(i):-</em></u>
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
<em>Null hypothesis :-</em>
<em> H₀ : μ = 18.0 c.m</em>
<em>Alternative Hypothesis:</em>
<em> H₁ : μ ≠ 18.0 c.m</em>
<em></em>
Test statistic
|Z| = |-2.688|
|Z| = 2.688≅ 2.7
<u><em>Step(ii):-</em></u>
<u><em>P -value :-</em></u>
<u><em>The z-test statistic value = 2.7</em></u>
<em>P( Z>2.7) = 1- P(Z< 2.7)</em>
<em> </em> = 1- ( 0.5+ A(2.7))
= 0.5 - A(2.7)
= 0.5 - 0.4965
<em> = 0.0035</em>
<em>P( Z>2.688)= 0.0035</em>
<em>Given data is two tailed test</em>
<em> 2 X P( Z>2.688) = 2 X 0.035 = 0.007</em>
<u><em>P-value = 0.007</em></u>
<u><em>we will choose level of significance ∝=0.05</em></u>
P -value < 0.05
H₀ is rejected
<em>Alternative Hypothesis is accepted </em>
<u><em>Final answer:-</em></u>
<em> The population mean of pencils produced in that factory have a mean length is not equal to 18.0 cm. </em>