Answer:
There is sufficient evidence that the students claim is correct.
Step-by-step explanation:
From the information given:
The population proportion P = 55% = 0.55
The sample size n = 150
The sample mean x = 96
The sampling proportion from the sample mean [tex]\hat p = \dfrac{x}{n}[/tex]
[tex]\hat p = \dfrac{96}{150}[/tex]
[tex]\hat p =0.64\\[/tex]
The null and alternative hypothesis is:
[tex]H_o : p = 0.55 \\ \\ H_1 : p > 0.55[/tex]
The test statistics can be computed as follows:
[tex]Z = \dfrac{\hat p - p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
[tex]Z = \dfrac{0.64 - 0.55}{\sqrt{\dfrac{0.55(1-0.55)}{150}}}[/tex]
[tex]Z = \dfrac{0.09}{\sqrt{\dfrac{0.2475}{150}}}[/tex]
[tex]Z = \dfrac{0.09}{\sqrt{0.00165}}[/tex]
Z = 2.22
The P - value = P ( Z > 2.22)
= 1 - P( Z < 2.22)
= 1 - 0.98679
= 0.01321
Since P-value is less than the level of significance ∝ = 0.05
We reject the null hypothesis [tex]H_o[/tex]
Conclusion: There is sufficient evidence that the students claim is correct.
