Pregunta: ¡Hola! Estoy repasando para mi final de STATS. ¡Por favor ayúdame a entender! ¡¡¡¡Gracias!!!!

Practice problem (Hypothesis test for a population proportion) 1. The manufacturer of alkaline batteries wants to be reasonably certain that fewer than $5\%$ of its batteries are defective. 400 batteries are randomly selected from a very large shipment, each is tested, and 12 defective batteries are found. Does this provide sufficient evidence for the manufacturer to conclude that the fraction of defective batteries in the entire shipment is less than 0.05 ? Use $=0.10$. a) Define, in terms of the problem, the parameter to be tested. b) State the null and alternate hypotheses using symbols. c) Calculate the appropriate test statistic d) Find the critical value and rejection region. e) Determine the p-value (the observed significance level). 0) Make decision. g) State the conclusion in terms of the problem. 2. It is claimed that $86\%$ of freshman students receive financial aid. If a survcy of 1000 freshman students showed that 893 of them receive financial aid, does this indicate that the percentage is not $86\%$ ? Test at 0.05 level of significance. a) Define, in terms of the problem, the parameter to be tested. b) State the null and alternate hypotheses using symbols. c) Calculate the apptopriate test statistic ब) Find the critical value and rejection region. c) Determine the p-value (the observed significance level). f Make decision. g) State the conclusion in terms of the problem. 1. The Lays potato chip factory has added a new machine which fills spack-pack sized bags of potato chips. The machine is supposed to put an average of 28.3 grams of chips in the bags it fills, but a quality control manager working at Lays believes the machine is overfilling the bags. A random sample of 25 bags filled by the machine had a mean of 28.7 grams and a standard deviation of 0.9 grams. Use a $1\%$ significance level to test the chaim that the machine is overfilling the " 28,3 gram" bags of chips a) Define, in terms of the problem, the parameter to be tested. b) State the null and alternate hypotheses using symbols. c) Calculate the appropriate test statistic d) Find the critical value and rejection region. e) Determine the p-value (the observed significance level). 0) Make decision. 8) State the conclusion in terms of the problem. 2. The company General Electric claims that, on average, a certain brand of its flashlight battery provides at least 300 hours of use. A researcher suspects that the population of batteries has a mean that is less than 300 hours. She selects a random sample of 49 barteries and obtains a sample mean of 290 hours and a sample standard deviation of 70 bours. Use the data to test the researcher's claim that the mean is less than 300 hours at a $5\%$ significance level. a) Define, in terms of the problem, the parameter to be tested. b) State the null and alternate hypotheses using symbols. c) Calculate the appropriate test statistic d) Find the critical value and rejection region. e) Determine the p-value (the observed significance level). 0) Make decision. B) State the conclusion in terms of the problem. 3. Data published by California on the salaries of state workers indicate the average yearly salary of fulltime secretarial staff at state universities is $\$47,500$. A sample of 64 full-time secretaries working for CSUL.A gencrates a mean of $\$49,000$ and a standard deviation of $\$6,200$. Use the data and a $5\%$ significance level to test whether the mean salary for secretarial staff at CSULA is different from the state mean.