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Answer:
The 95% confidence interval for true proportion of red candies is (5%, 27%).
The true proportion of red candies made by the company is different from 33%.
Step-by-step explanation:
The hypothesis to determine whether the claim made by the candy company is correct or not is:
<em>H</em>₀: The true proportion of red candies made by the company is 33%, i.e. <em>p</em> = 0.33.
<em>Hₐ</em>: The true proportion of red candies made by the company is different from 33%, i.e. <em>p</em> ≠ 0.33.
A (1 - <em>α</em>)% confidence interval can be constructed to check this claim.
The decision rule is:
If the confidence interval consists the null value then the null hypothesis will not be rejected. Otherwise it will be rejected.
The (1 - <em>α</em>)% confidence interval for population proportion is:
The information provided is:
<em>n</em> = 42
<em>X</em> = number of red candies = 7
Compute the sample proportion of candies that are red as follows:
The critical value of <em>z</em> for 95% confidence level is:
*Use a <em>z</em>-table for the critical value.
Compute the 95% confidence interval for true proportion of red candies as follows:
The 95% confidence interval for true proportion of red candies is (5%, 27%).
The confidence interval does not contains the null value.
Thus, the null hypothesis will be rejected at 5% level of significance.
Conclusion:
The true proportion of red candies made by the company is different from 33%.