Question

Fowle Marketing Research, Inc., bases charges to a client on the
assumption that telephone surveys can be completed in a mean time
of 15 minutes or less. If a longer mean survey time is necessary, a
premium rate is charged. Suppose a sample of 35 surveys produces
the data in the Microsoft Excel Online file below. Use a known
*σ* = 3.5 minutes. Is the premium rate justified?

Call Time (minutes) |

20.3 |

13.7 |

16.2 |

18.1 |

13.8 |

17.3 |

14.6 |

17.4 |

18.5 |

10.5 |

15.1 |

16.6 |

17 |

14.5 |

20 |

11.3 |

16.3 |

20.5 |

21.7 |

16 |

12.2 |

18.5 |

25.9 |

14.5 |

21.6 |

15.6 |

15.9 |

14.7 |

17.6 |

18 |

16.7 |

11.6 |

16.8 |

13 |

13.2 |

a. Formulate the null and alternative hypotheses for this application.

*H*_{0}: *μ ? ___*

*H*_{a}: *μ ? ___*

b.Compute the value of the test statistic (to 2 decimals).

c.What is the *p*-value (to 4 decimals)?

d.Using ? = .01, is a premium rate justified for this client?

yes or no?

Answer #1

First enter Data into EXCEL

We have to find the sample mean.

Excel command is =AVERAGE(Select data)

sample mean = 16.43

n = 35

claim :premium rate justified for this client

a)

Null and alternative hypothesis is

Level of significance = 0.01

b)

Here population standard deviation is known so we use z-test statistic.

Test statistic is

Degrees of freedom = n - 1 = 35-1=34

c)

P-value =0.00776. ( using z table)

The P-Value is 0 .0078

P-value , Reject H0

**d)**

**conclusion :**Yes Using ? = .01, premium rate
justified for this client.

Fowle Marketing Research, Inc., bases charges to a client on the
assumption that telephone surveys can be completed in a mean time
of 15 minutes or less. If a longer mean survey time is necessary, a
premium rate is charged. Suppose a sample of 35 surveys produces
the data in the Microsoft Excel Online file below. Use a known σ =
3.8 minutes. Is the premium rate justified? Open spreadsheet
Formulate the null and alternative hypotheses for this application.
H0:...

Fowle Marketing Research, Inc., bases charges to a client on the
assumption that telephone surveys can be completed in a mean time
of 15 minutes or less. If a longer mean survey time is necessary, a
premium rate is charged. Suppose a sample of 35 surveys produces
the data in the Microsoft Excel Online file below. Use a known σ =
3.7 minutes. Compute the value of the test statistic (to 2
decimals). 2.32 What is the p-value (to 4...

Fowle Marketing
Research, Inc., bases charges to a client on the assumption that
telephone surveys can be completed within an average time of 15
minutes or less. If more time is required, a premium rate is
charged.
The testable hypotheses in this situation are
H0:μ=15H0:μ=15 vs.
Ha:μ>15Ha:μ>15
1. Identify the consequences of making a Type I
error.
A. The company charges the customer the premium
rate when they should.
B. The company does not charge the customer the
premium rate...

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