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:
<u><em>Step(i):-</em></u>
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
![p = \frac{x}{n} = \frac{501}{934} = 0.5364](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7Bx%7D%7Bn%7D%20%3D%20%5Cfrac%7B501%7D%7B934%7D%20%3D%200.5364)
Level of significance = 0.05
Critical value Z₀.₀₅ = 1.96
<u><em>Step(ii):-</em></u>
Null hypothesis: P < 0.51
Alternative Hypothesis : P > 0.51
Test statistic
![Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7Bp-P%7D%7B%5Csqrt%7B%5Cfrac%7BPQ%7D%7Bn%7D%20%7D%20%7D)
![Z = \frac{0.536-0.51}{\sqrt{\frac{0.51 x 0.49}{934} } }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B0.536-0.51%7D%7B%5Csqrt%7B%5Cfrac%7B0.51%20x%200.49%7D%7B934%7D%20%7D%20%7D)
Z = 1.5950
<u><em>Final answer:-</em></u>
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