Question

A company using the newly installed automation software claims that the software can correct itself 55% of the times. The quality control manager believes the percentage is lower. She presented a report of 950 glitches in which 477 were automatically corrected. Test this hypothesis at the 0.01 significance level. Perform the following steps of hypotheses testing and draw a conclusion.

Answer 1

To test the hypothesis that the software can correct itself with a probability of 55%, we perform a hypothesis test. The null hypothesis is that the software can correct itself with a probability of 55%. The alternative hypothesis is that the software cannot correct itself with a probability of 55%.

Step-by-step explanation:

To test the hypothesis that the software can correct itself with a probability of 55%, we need to perform a hypothesis test. Let's define the null and alternative hypotheses:

Null Hypothesis (H0): The software can correct itself with a probability of 55%.

Alternative Hypothesis (H1): The software cannot correct itself with a probability of 55%.

Next, we calculate the test statistic and p-value using the provided data. In this case, the test statistic is a z-score for the sample proportion. The formula to calculate the z-score is (p - P) / √[(P * (1 - P)) / n].

Here, p is the sample proportion (477/950), P is the hypothesized proportion (0.55), and n is the sample size (950).

Once we have the z-score, we can find the p-value using a standard normal distribution table or a calculator.

If the p-value is less than the significance level (0.01), we reject the null hypothesis.

If the p-value is greater than or equal to the significance level, we fail to reject the null hypothesis.

Based on the provided information, the p-value is 0.0067, which is less than the significance level of 0.01. Therefore, we reject the null hypothesis.

This means that there is enough evidence to support that the software can correct itself with a probability that is different from 55%.