## Related questions with answers

**Effectiveness of skin cream**. Pond's Age-Defying Complex, a cream with alpha hydroxy acid, advertised that it could reduce wrinkles and improve the skin. In a study published in Archives of Dermatology (June 1996), 33 middle-aged women used a cream with alpha hydroxy acid for 22 weeks. At the end of the study period, a dermatologist judged whether each woman exhibited skin improvement. The results for the 33 women (where $I=$ improved skin and $\mathrm{N}=$ no improvement) are listed in the next table. [Note: Pond's recently discontinued the production of this cream product, replacing it with Age-Defying Towlettes.] Find and interpret the $p$-value of the test.

$\mathrm{I}$ | $\mathrm{I}$ | $\mathrm{N}$ | $\mathrm{I}$ | $\mathrm{N}$ | $\mathrm{N}$ | $\mathrm{I}$ | $\mathrm{I}$ | $\mathrm{I}$ | $\mathrm{I}$ | $\mathrm{I}$ | $\mathrm{I}$ |
---|---|---|---|---|---|---|---|---|---|---|---|

$\mathrm{N}$ | $\mathrm{I}$ | $\mathrm{I}$ | $\mathrm{I}$ | $\mathrm{N}$ | $\mathrm{I}$ | $\mathrm{I}$ | $\mathrm{I}$ | $\mathrm{N}$ | $\mathrm{I}$ | $\mathrm{N}$ | $\mathrm{I}$ |

$\mathrm{I}$ | $\mathrm{I}$ | $\mathrm{I}$ | $\mathrm{I}$ | $\mathrm{I}$ | $\mathrm{N}$ | $\mathrm{I}$ | $\mathrm{I}$ | $\mathrm{N}$ |

Solution

VerifiedFirst, identify the null and alternative hypotheses of this test.

**$H_0$**: The true proportion of middle-aged women with improved skin by using the Pond's Age-Defying Complex is 60%. ($p = 0.6$)
**$H_a$**: The true proportion of middle-aged women with improved skin by using the Pond's Age-Defying Complex is more than 60%. ($p >0.6$)

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