Answer:
a. 0.1576<p<0.2310
b. The two restaurants likely have similar order rates which are inaccurate.
Step-by-step explanation:
a. We first calculate the proportion, [tex]\hat p[/tex]:
[tex]\hat p=\frac{61}{314}\\\\=0.1943[/tex]
-We use the z-value alongside the proportion to calculate the margin of error:
[tex]MOE=z\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\=1.645\times \sqrt{\frac{0.1943(1-0.1943)}{314}}\\\\=0.0367[/tex]
The confidence interval at 90% is then calculated as:
[tex]CI=\hat p\pm MOE\\\\=0.1943\pm 0.0367\\\\=[0.1576,0.2310][/tex]
Hence, the confidence interval at 90% is [0.1576,0.2310]
b. From a above, the calculated confidence interval is 0.1576<p<0.2310
-We compare the calculated CI to the stated CI of 0.147<p<0.206
-The two confidence intervals overlap each other and have the same value for 0.1576<p<0.206
-Hence, we conclude that the two restaurants likely have similar order rates which are inaccurate.
