Question

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%.

Answer 1

See below for all information

Explanation:

Given Information

• Observed Sample Proportion:
  `p=(33)/(362)\approx0.0912`
• Hypothesized Population Proportion:
  `p_0=0.10`
• Sample Size:
  `n=362`
• Significance Level:
  `\alpha=0.05`
• 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:
  `H_0:p=0.10` (this tells us that the actual proportion of inaccurate orders of 10% is equal to the observed proportion of inaccurate orders)
• Alternate:
  `H_1:p\\eq0.10` (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

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

Determine p-value from z-statistic

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

Draw conclusion of p-value based on given significance level

Since
`p > 0.05`, 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.