The Filling Machine For A Production Operation Must Be Adjusted The Filling Machine For A Production Operation Must Be Adjusted The filling machine for a production operation must be adjusted if more than 10% of the items being produced are under filled. A random sample of 100 items from day’s production contained 16 under filled items. Does the sample evidence indicate that the filling machine should be adjusted? Conduct an appropriate test of hypotheses for the population proportion using an alpha value of .05. Use Minitab output to help answer. - Write the null and alternative hypotheses. - State the rejection rule for the null hypothesis using the “critical value method to test hypothesis”. - State the rejection rule for the null hypothesis using the “p-value method to test hypothesis”. - State your statistical conclusion as it relates to the problem and in words relating to the problem.
Paper For Above instruction The scenario involves assessing whether a filling machine requires adjustment based on the proportion of underfilled items it produces. The core statistical question is whether the true proportion of underfilled items exceeds the acceptable threshold of 10%. To analyze this, a hypothesis test for the population proportion provides a systematic approach. Null and Alternative Hypotheses The null hypothesis (H■) assumes that the machine’s underfilled rate is at or below the threshold of 10%. Mathematically, this is expressed as: H■: p ≤ 0.10 The alternative hypothesis (H■) posits that the true proportion exceeds 10%, suggesting the machine needs adjustment: H■: p > 0.10 Rejection Rule Using the Critical Value Method At a significance level (α) of 0.05, the critical z-value for a one-tailed test can be found from standard normal distribution tables, approximately 1.645. The rejection rule states that if the calculated z-value from