Question

A drug, which is used for treating cancer, has potentially dangerous side effects if it is taken in doses which are larger than 47.87mg, the required dosage for the treatment. It is important that the variance of the amount of the active ingredient is 0.04. 15 tablets are randomly selected and the amount of the drug in each tablet is measured. It is determined that the variance of the amount of active ingredient is 0.0008mg. Does the data suggests at α=0.025 that the variance of the drug in the tablets is less than the desired amount? Assume the population is normally distributed.

Step 1 of 5: State the null and alternative hypotheses. Round to four decimal places when necessary.

Step 2 of 5: Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.

Step 3 of 5: Determine the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Make the decision

Step 5 of 5: What is the conclusion?

Answer #1

step 1"

Ho:
σ^{2} |
= | 0.04 |

Ha:
σ^{2} |
≠ | 0.04 |

Step 2 of 5:

for 2.5 % level and (n-1=14) df critical values of X2 = |
5.629 |

Step 3 of 5:

test statistic X2 =(n-1)s^{2}/ σ^{2}= |
0.2800 |

Step 4 of 5:

since test statistic falls in rejection region we reject null hypothesis |

Step 5 of 5:

we have sufficient evidence to conclude that variance of the drug in the tablets is less than the desired amount |

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