Edit in JSFiddle

  const vm = new Vue({
    el: "#app",
    data: {
      list: ["接客", "清潔感", "早さ", "雰囲気", "味", "値段", "空調"],
      index: 0,
      a: null,
      show: false,
      answers: [],
    },
    methods: {
      next: function(e) {
        this.answers.push(this.a)
        _.delay(() => { this.index++; this.a = null }, 500)
      },
    },
    computed: {
      q: function() {
        return this.list[this.index % this.list.length]
      },
    },
  })
<div id="app">
  <template v-if="!show">
    <div class="btn btn-primary" @click="show = true">
      応募
    </div>
  </template>
  <template v-else="">
    <div class="panel panel-info">
      <div class="panel-heading">
        アンケートに協力お願いします
      </div>
      <div class="panel-body">
        <p>
          {{q}}はいかがでしたか?
        </p>
        <label class="radio-inline">
          <input type="radio" v-model.number="a" @change="next" value="-1">悪い
        </label>
        <label class="radio-inline">
          <input type="radio" v-model.number="a" @change="next" value="0">普通
        </label>
        <label class="radio-inline">
          <input type="radio" v-model.number="a" @change="next" value="1">良い
          </label>
      </div>
    </div>
    {{answers}}
  </template>
</div>