Question: In a marketing survey for an automobile manufacturer, 90 randomly selected adults are asked which car color they would choose, if a particular car were available in either blue or red body colors. Of the 90 respondents, 53 said "blue."

1. Let p = population proportion that would say "blue." The manufacturer wants to learn if a majority of buyers would pick blue. Keeping in mind that a majority is p>0.5, write a null and alternative hypothesis about p in this situation. (Hint: What somebody wants to "prove" is usually the alternative.)
2. What is the value of \[\hat{p}\] =sample proportion that picked blue?
3. Test the hypotheses stated in part a above. By hand, calculate the test statistic by using (Notice that this statistic is sensitive to the difference between the sample result and the null hypothesis value):
   \[z=\frac{\text{sample p - null hyp}\text{. p}}{\text{null std}\text{. error}}=\frac{\hat{p}-{{p}_{0}}}{\sqrt{\frac{{{p}_{0}}(1-{{p}_{0}})}{n}}}\] (round your final value to two decimal places)
4. Use the Standard Normal Table to find the p-value associated with this test statistic. Use the p-value guidelines found at the beginning of this activity.
5. In Minitab use Stat>Basic Stats>1 proportion , click Summarized Data , enter 90 for number of trials and 53 for Number of events. Click on Perform Hypothesis Test and enter 0. 50 where it says "Hypothesized proportion" AND click Options to select the alternative hypothesis as "greater than" AND also click on "Use test and interval based on normal distribution."
   What value is given for test statistic in the output? _______ What is the p-value? ______
   1. Do the Z test statistic you found by hand in part c and the p-value from part d approximately equal to the Z statistic found in part e when using Minitab?
   2. Decide whether the result is significant based on the p-value from Minitab and report a conclusion in the context of this situation.

iii What would the p-value have been if manufacturer wanted to test if a equal proportion of red and blue cars would be purchased? That is, test Ho: p = 0.5 versus Ha: p ≠ 0.5

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