Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 290 engines and the mean pressure was 7.6 pounds/square inch (psi). Assume the population standard deviation is 1.0. If the valve was designed to produce a mean pressure of 7.7 psi, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications?

Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

Step 4 of 6: Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6: Identify the level of significance for the hypothesis test.

Step 6 of 6: Make the decision to reject or fail to reject the null hypothesis.

Answer #1

Step 1 of 6:

null hypothesis:Ho μ | = | 7.7 | |

Alternate Hypothesis:Ha μ | ≠ | 7.7 |

Step 2 of 6:

population mean μ= | 7.7 |

sample mean 'x̄= | 7.600 |

sample size n= | 290.00 |

std deviation σ= | 1.000 |

std error ='σx=σ/√n= | 0.0587 |

test stat z = '(x̄-μ)*√n/σ= |
-1.70 |

Step 3 of 6:

two-tailed.

Step 4 of 6:

p value = | 0.0892 |

Step 5 of 6:

level of significance for the hypothesis test =0.02

Step 6 of 6:

fail to reject the null hypothesis.

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