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The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the following school year. She wants to know if each type of food will be equally popular so she can start ordering supplies and making other plans. To find out, she selects a random sample of 100 students and asks them, "Which type of food do you prefer: Asian food, Mexican food, pizza, or hamburgers?" Here are her data:

 Type of Food:  Asian  Mexican  Pizza  Hamburgers  Count: 18223921\scriptstyle\begin{array}{lcccc} \hline \text { Type of Food: } & \text { Asian } & \text { Mexican } & \text { Pizza } & \text { Hamburgers } \\ \text { Count: } & 18 & 22 & 39 & 21 \\ \hline \end{array}

An appropriate null hypothesis to test whether the food choices are equally popular is (a) H0:μ=25,H_{0}: \mu=25, where μ\mu = the mean number of students that prefer each type of food. (b) H0:p=0.25,H_{0}: p=0.25, where p = the proportion of all students who prefer Asian food. (c) H0:nA=nM=nP=nH=25,H_{0}: n_{A}=n_{M}=n_{P}=n_{H}=25, where nAn_{A} is the number of students in the school who would choose Asian food, and so on. (d) H0:pA=pM=pP=pH=0.25,H_{0}: p_{A}=p_{M}=p_{P}=p_{H}=0.25, where pAp_{A} is the proportion of students in the school who would choose Asian food, and so on. (e) H0:p^A=p^M=p^P=p^H=0.25,H_{0}: \hat{p}_{A}=\hat{p}_{M}=\hat{p}_{P}=\hat{p}_{H}=0.25, where p^A\hat{p}_{A} is the proportion of students in the sample who chose Asian food, and so on.

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What are the advantages and disadvantages of using observations, standardized tests, and case studies to collect data?

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The case studies collect information from various sources and use multiple methods. That information may be used for creating new hypotheses.

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