Question

The dosage of a drug in a particular tablet needs to be precise. It is essential that the tablets contain 59.21mg of the active ingredient with a variance of 0.02. A random sample of 18 tablets finds that the variance of the active ingredient is 0.0118. 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. A: Reject Null Hypothesis B: Fail to Reject Null Hypothesis

Step 5 of 5: What is the conclusion? There is sufficient evidence to show that the amount of active ingredient has a variance that is less than the desired amount. There is not sufficient evidence to show that the amount of active ingredient has a variance that is less than the desired amount.

Answer #1

1)

Ho:
σ^{2} |
>= | 0.02 |

Ha:
σ^{2} |
< | 0.02 |

2)

for 2.5 % level and given df critical values of X2 = | 7.564 |

3)

test statistic X2 =(n-1)s^{2}/
σ^{2}=(18-1)*(0.0118/0.02) = |
10.030 |

4)

since test statistic does not falls in rejection region we fail to reject null hypothesis |

5)

There is not sufficient evidence to show that the amount of active ingredient has a variance that is less than the desired amount.

The dosage of a drug in a particular tablet needs to be precise.
It is essential that the tablets contain 59.21mg of the active
ingredient with a variance of 0.022. A random sample of 18 tablets
finds that the variance of the active ingredient is 0.0118. 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.
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