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About 30% of the population cannot detect any odor when they sniff the steroid androstenone, but they can become sensitive to its smell if exposed to the chemical repeatedly. . After the 21 days, the researchers found that 10 of 12 participants had improved androstenone-detection accuracy

Sagot :

Using the z-distribution, as we are working with a proportion, it is found that there is enough evidence to conclude that the proportion is different of 50%.

What are the hypothesis tested?

At the null hypothesis, it is tested if the proportion is of 0.5, that is:

[tex]H_0: p = 0.5[/tex]


At the alternative hypothesis, it is tested if the proportion is different of 0.5, that is:

[tex]H_1: p \neq 0.5[/tex].

What is the test statistic?

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

  • [tex]\overline{p}[/tex] is the sample proportion.
  • p is the proportion tested at the null hypothesis.
  • n is the sample size.

In this problem, the parameters are:

[tex]p = 0.5, n = 12, \overline{p} = \frac{10}{12} = 0.8333[/tex]

Then, the value of the test statistic is as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.8333 - 0.5}{\sqrt{\frac{0.5(0.5)}{12}}}[/tex]

[tex]z = 2.31[/tex]

What is the decision?

Considering a two-tailed test, as we are testing if the proportion is different of a value, with a significance level of 0.05, the critical value is of [tex]|z^{\ast} = 1.96[/tex].

Since the absolute value of the test statistic is greater than the critical value for the two-tailed test, it is found that there is enough evidence to conclude that the proportion of participants that had improved androstenone-detection accuracy is different of 50%.

More can be learned about the z-distribution at https://brainly.com/question/26454209

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