STATISTICS MATH PLS HELP - In a study of the accuracy of fast food drive through orders, McDonald’s had 33 orders that were not accurate among 362 orders observed. Use a 0.05 significance level to test the claim that the rate of inaccurate orders is equal to 10%.

Observed Sample Proportion: [tex]p=\frac{33}{362}\approx0.0912[/tex]
Hypothesized Population Proportion: [tex]p_0=0.10[/tex]
Sample Size: [tex]n=362[/tex]
Significance Level: [tex]\alpha=0.05[/tex]
We should conduct a two-tailed one-proportion z-test (remember to double the p-value to consider both tails!)
Assume conditions are met

Null and Alternate Hypotheses

Null: [tex]H_0:p=0.10[/tex] (this tells us that the actual proportion of inaccurate orders of 10% is equal to the observed proportion of inaccurate orders)
Alternate: [tex]H_1:p\neq0.10[/tex] (this tells us that the actual proportion of inaccurate orders of 10% is NOT equal to the observed proportion of inaccurate orders)

Determine z-statistic

[tex]\displaystyle Z=\frac{p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}=\frac{\frac{33}{362}-0.10 }{\sqrt{\frac{0.10(1-0.10)}{362}}}\approx-0.5606[/tex]

Determine p-value from z-statistic

[tex]2\cdot P(Z < -0.5606)=2\cdot\text{normalcdf}(-1E99,-0.5606)\approx2\cdot0.28753\approx0.5751[/tex]

Draw conclusion of p-value based on given significance level

Since [tex]p > 0.05[/tex], we fail to reject the null hypothesis. This means that we do have sufficient evidence to say that the observed rate of inaccurate orders is equal to 10%, making it extremely likely that the null hypothesis is true.