A scientist for a company that manufactures processed food wants to assess the percentage of fat in the company's bottled sauce. The advertised percentage is 15%. The scientist measures the percentage of fat in 20 random samples. Previous measurements found that the population standard deviation is 2.6%.

The scientist performs a 1-sample Z-test to determine whether the fat percentage differs from 15%.

- Open the sample data, FatContent.MTW.
- Choose .
- From the drop-down list, select One or more samples, each in a column and enter Percent Fat.
- In Known standard deviation, enter
`2.6`. - Select Perform hypothesis test.
- In Hypothesized mean, enter
`15`. - Click OK.

The null hypothesis states that the mean of the percentage of fat equals 15%. Because the p-value is 0.012, which is less than the significance level of 0.05, the scientist rejects the null hypothesis. The results indicate that mean percentage of fat differs from 15%.

N | Mean | StDev | SE Mean | 95% CI for μ |
---|---|---|---|---|

20 | 16.460 | 2.258 | 0.581 | (15.321, 17.599) |

Null hypothesis | H₀: μ = 15 |
---|---|

Alternative hypothesis | H₁: μ ≠ 15 |

Z-Value | P-Value |
---|---|

2.51 | 0.012 |