Hypothesis Testing – Z-test

Question 3:

In a certain country it is known that the time it takes to feel better after a certain illness is normally distributed with a mean of 7 days, and a standard deviation of 1.55 days.

A researcher reported that she treated 89 patients, and the average duration it took to heal is 6.67.

Based upon that information, is there a strong enough evidence to conclude that the actual healing time is actually shorter than what is currently known?

Check under 5% level of significance and under 1% level of significance.

Answer 3:

Set of hypotheses:

Since the population’s standard deviation is known, we need to use Z-test and not t-test.

There’s the Statistic value–

From the Z-table the relevant P-value for that left-tailed hypothesis –

Conclusion:

At 5% level of significance, there’s strong enough evidence to reject the null hypothesis, however at 1% level of significance, there’s no strong enough evidence to reject the null hypothesis.

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