In a study of the accuracy of fast food drive-through orders, one restaurant had 38 orders…
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Question “In a study of the accuracy of fast food drive-through orders, one restaurant had 38 orders…”
Answer
Solution:
This is the two-tailed test.
Alternative hypothesis and the null hypothesis are
H : p = 0.10
![In a study of the accuracy of fast food drive-through orders, one restaurant had 38 orders...](https://drive.google.com/uc?id=1dpNA1BPmetKa8w44QJA1He2jHckE8woi&export=download/In-a-study-of-the-accuracy-of-fast-food-drive-through-orders,-one-restaurant-had-38-orders.png?x-oss-process=image/resize,w_560/format,webp)
0.10
n = 338
x = 38
= x / 38 / 338 =0.11
P0 = 0.10
1 – P0 = 1 – 0.10 = 0.90
Test statistic = z
=
![In a study of the accuracy of fast food drive-through orders, one restaurant had 38 orders...](https://drive.google.com/uc?id=16QoL5qbAFdUT8LrqHXHq_hqoA_8fhkpd&export=download/In-a-study-of-the-accuracy-of-fast-food-drive-through-orders,-one-restaurant-had-38-orders.gif?x-oss-process=image/resize,w_560/format,webp)
– P0 / [
![In a study of the accuracy of fast food drive-through orders, one restaurant had 38 orders...](https://drive.google.com/uc?id=1S5Z1NC_HyroTaJizBN8VpBvi0fym8hU0&export=download/In-a-study-of-the-accuracy-of-fast-food-drive-through-orders,-one-restaurant-had-38-orders.gif?x-oss-process=image/resize,w_560/format,webp)
P0 * (1 – P0 ) / n]
![In a study of the accuracy of fast food drive-through orders, one restaurant had 38 orders...](https://drive.google.com/uc?id=1S5Z1NC_HyroTaJizBN8VpBvi0fym8hU0&export=download/In-a-study-of-the-accuracy-of-fast-food-drive-through-orders,-one-restaurant-had-38-orders.gif?x-oss-process=image/resize,w_560/format,webp)
(0.10*0.90) /338 ]
= 0.76
Test statistic = z = 0.76
P(z > 0.76 ) = 1 – P(z < 0.76 ) = 0.7764
P-value = 2 * 0.2236 = 0.4472
![In a study of the accuracy of fast food drive-through orders, one restaurant had 38 orders...](https://drive.google.com/uc?id=1n6EcAeDy1RDCM7hCmZK2x-VHVOZwBTJk&export=download/In-a-study-of-the-accuracy-of-fast-food-drive-through-orders,-one-restaurant-had-38-orders.png?x-oss-process=image/resize,w_560/format,webp)
= 0.05
![In a study of the accuracy of fast food drive-through orders, one restaurant had 38 orders...](https://drive.google.com/uc?id=1n6EcAeDy1RDCM7hCmZK2x-VHVOZwBTJk&export=download/In-a-study-of-the-accuracy-of-fast-food-drive-through-orders,-one-restaurant-had-38-orders.png?x-oss-process=image/resize,w_560/format,webp)
0.4472 > 0.05
Reject the null hypothesis.
The claim that 10% of orders are incorrect is unsupported by sufficient evidence
The resturant should not be allowed to reject the claim that 10% is the rate of inaccurate orders, as there isn’t enough evidence.
Conclusion
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