Respuesta :
Answer:
The calculated value Z = 1.5950 < 1.96 at 0.05 level of significance
The null hypothesis is accepted at a 0.05 level of significance
The proportion of cell phone owners in that country who have a smartphone has not increased over time
Step-by-step explanation:
Step(i):-
Given that the random sample size 'n' = 934
Given that the population proportion P = 0.51
Q= 1-P
Q = 1- 0.51 = 0.49
The sample proportion
[tex]p = \frac{x}{n} = \frac{501}{934} = 0.5364[/tex]
Level of significance = 0.05
Critical value Z₀.₀₅ = 1.96
Step(ii):-
Null hypothesis: P < 0.51
Alternative Hypothesis : P > 0.51
Test statistic
[tex]Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }[/tex]
[tex]Z = \frac{0.536-0.51}{\sqrt{\frac{0.51 x 0.49}{934} } }[/tex]
Z = 1.5950
Final answer:-
Given that P-value 0. 0532
P-value > 0.05
Rejected Alternative Hypothesis and accepted null hypothesis
( OR)
The calculated value Z = 1.5950 < 1.96 at 0.05 level of significance
The null hypothesis is accepted at a 0.05 level of significance
The proportion of cell phone owners in that country who have a smartphone has not increased over time
