Question

In a study of the accuracy of fast food drive-through orders, Restaurant A had

245245

accurate orders and

6666

that were not accurate.

a. Construct a

9090%

confidence interval estimate of the percentage of orders that are not accurate.

b. Compare the results from part (a) to this

9090%

confidence interval for the percentage of orders that are not accurate at Restaurant B:

0.1920.192less than<pless than<0.2750.275.

What do you conclude?

Answer #1

Total orders = 245 + 66 = 311

a) The sample proportion of orders that are not accurate is
computed here as:

p = x/n = 66/311 = 0.2122

From standard normal tables, we have:

P( -1.645 < Z < 1.645) = 0.9

Therefore the 90% confidence interval here is computed as:

**Therefore 17.41%, 25.03% is the required 90% confidence
interval here for the percentage of orders that are not
accurate.**

b) For restaurant B, we have here:

0.192 < p < 0.275

The confidence interval for B does not wholly lie above the confidence interval for A nor does the whole confidence interval lies below the lower value for confidence interval for A.

**Therefore we cannot conclude anything from the
given interval.**

In a study of the accuracy of fast food drive-through orders,
Restaurant A had
336336
accurate orders and
7171
that were not accurate.
a. Construct a
9090%
confidence interval estimate of the percentage of orders that
are not accurate.
b. Compare the results from part (a) to this
9090%
confidence interval for the percentage of orders that are not
accurate at Restaurant B:
0.1630.163less than<pless than<0.2190.219.
What do you conclude?

In a study of the accuracy of fast food drive-through orders,
Restaurant A had
343343
accurate orders and
5252
that were not accurate.
a. Construct a
9090%
confidence interval estimate of the percentage of orders that
are not accurate.
b. Compare the results from part (a) to
this
9090%
confidence interval for the percentage of orders that are not
accurate at Restaurant B:
0.1190.119less than<pless than<0.1740.174.
What do you conclude?

In a study of the accuracy of fast food drive-through orders,
Restaurant A had
241241
accurate orders and
6565
that were not accurate.
a. Construct a
9595%
confidence interval estimate of the percentage of orders that
are not accurate.
b. Compare the results from part (a) to this
9595%
confidence interval for the percentage of orders that are not
accurate at Restaurant B:
0.1860.186less than<pless than<0.2780.278.
What do you conclude?

In a study of the accuracy of fast food drive-through orders,
Restaurant A had
340340
accurate orders and
6060
that were not accurate.
a. Construct a
9595%
confidence interval estimate of the percentage of orders that
are not accurate.
b. Compare the results from part (a) to this
9595%
confidence interval for the percentage of orders that are not
accurate at Restaurant B:
0.1350.135less than<pless than<0.2010.201.
What do you conclude?

In a study of the accuracy of fast food drive-through orders,
Restaurant A had 304 accurate orders and
72 that were not accurate. a. Construct a 90%
confidence interval estimate of the percentage of orders that are
not accurate. b. Compare the results from part
(a) to this
90% confidence interval for the percentage of orders that are
not accurate at Restaurant B: 0.1730.173less than<pless
than<0.2470.247. What do you conclude?
Express the percentages in decimal form.

In a study of the accuracy of fast food drive-through orders,
Restaurant A had 238 accurate orders and 58 that were not accurate.
a. Construct a 90% confidence interval estimate of the percentage
of orders that are not accurate. b. Compare the results from part
(a) to this 90% confidence interval for the percentage of orders
that are not accurate at Restaurant B: 0.174 less than p less than
0.259. What do you conclude?

In a study of the accuracy of fast food drive-through orders,
Restaurant A had
267
accurate orders and
72
that were not accurate.
a. Construct a
90%
confidence interval estimate of the percentage of orders that
are not accurate.
b. Compare the results from part (a) to this
90%
confidence interval for the percentage of orders that are not
accurate at Restaurant B:
0.1950 <0.262
What do you conclude?

In a study of the accuracy of fast food drive-through orders,
Restaurant A had 221 accurate orders and 64 that were not
accurate.
a. Construct a 95% confidence interval estimate of the
percentage of orders that are not accurate.
b. Compare the results from part (a) to this 95% confidence
interval for the percentage of orders that are not accurate at
Restaurant B: 0.196<p<0.304.
What do you conclude?

In a study of the accuracy of fast food drive-through orders,
Restaurant A had 296 accurate orders and 61 that were not accurate.
a. Construct a 95% confidence interval estimate of the percentage
of orders that are not accurate. b. Compare the results from part
(a) to this 95% confidence interval for the percentage of orders
that are not accurate at Restaurant B: 0.154 < p < 0.225.
What do you conclude?

In a study of the accuracy of fast food drive-through orders,
Restaurant A had 210 accurate orders and 67 that were not
accurate.
a. Construct a 90% confidence interval estimate of the
percentage of orders that are not accurate.
b. Compare the results from part (a) to this 90% confidence
interval for the percentage of orders that are not accurate at
Restaurant B: 0.222 <p< 0.307. What do you conclude?

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