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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%.

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Answer:

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.

User Graymatter
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