STA 2023 Calculator Instructions: Hypothesis Tests About the Mean and ProportionHypothesis Tests About the MeanHypothesis tests about means can be Z-based (if σ is known) or T-based (if σ is unknown and either the population is normal or the sample size is over 30). The TI calculators provide functions for both the Z-Test and the T-Test. They both provide a p-value for comparison with the test’s significance level. Since σ is rarely known, we will use the T-Test to perform our tests of significance. The T-Test is located on the STAT page in the Tests list. The menu for T-Test is very similar to the one for TInterval described in the last chapter. Again you have a choice between working with the data or the summary statistics. The T-Test requires you to enter the null hypothesis, the sample mean, and which alternative hypothesis you are using.Example: Auto BatteriesHypothesis Tests About ProportionsHypothesis tests about proportions are Z-based for sample sizes over 30. The calculator provides a function called 1-PropZTest that computes a test statistics and p-value. The 1-PropZTest is located on the STAT page under the Tests list. The menu for 1-PropZTest is very similar to the one for 1-PropZInt described in the last chapter. Again you need to enter x, the number of successes, and n, the sample size. You also need to enter p0, the number that p is being compared with, and the alternative hypothesis.When working properly, a machine that is used to make chips for calculators does not produce more than 4% defective chips. Whenever the machine produces more than 4% defective chips, it needs an adjustment. To check if the machine is working properly, the quality control department at the company often takes samples of chips and inspects them to determine if they are good or defective. One such sample of 200 chips taken recently from the production line contained 14 defective chips. Test at the 5% significance level whether or not the machine needs an adjustment.Hypothesis Tests About the Mean and ProportionExample: Quality ControlSTA 2023 Calculator Instructions: Hypothesis Tests About the Mean and ProportionHypothesis Tests About the MeanHypothesis tests about means can be Z-based (if σ is known) or T-based (if σ is unknown andeither the population is normal or the sample size is over 30). The TI calculators providefunctions for both the Z-Test and the T-Test. They both provide a p-value for comparison withthe test’s significance level. Since σ is rarely known, we will use the T-Test to perform our testsof significance. The T-Test is located on the STAT page in the Tests list. The menu for T-Test isvery similar to the one for TInterval described in the last chapter. Again you have a choicebetween working with the data or the summary statistics. The T-Test requires you to enter thenull hypothesis, the sample mean, and which alternative hypothesis you are using.Example: Mean SalaryAccording to a salary survey the average salary offered to computer science majors whograduated in May 2002 was $50,352. Suppose this result is true for all computer science majorswho graduated in May 2002. A random sample of 200 computer science majors who graduatedthis year showed they were offered a mean salary of $51,750 with a standard deviation of $5240.Using a 1% significance level, can you conclude that the mean salary of this year’s computerscience graduates is higher than $50,352? The null hypotheses is H0: µ = 50,352 and thealternative hypothesis is H1: µ > 50,352. We will use the T-Test, choosing Stats, with µ0 = 50,352,X = 51,750, sx = 5240, n = 200, and µ1 > µ0 for our alternative hypothesis.Press the STAT key.Press the ► key twice to highlight TESTS.Press the number 2 key.Move the cursor over Stats and press the ENTER key.Type in 50352 for μ0.Type in 51750 for X.Type in 5240 for Sx.Type in 200 for n.Move the cursor over >μ0 and press the ENTER key.Move the cursor over Calculate and press the ENTER key.The T-Test output shows the alternative hypothesis: μ>50352 test statistic: t=3.77303543 p-value: 1.0635428E-4 sample mean: X=51750 sample standard deviation: Sx=5240 sample size: n=2001The p-value is 1.064×10−4 which is less than 1%. We reject H0 and conclude that the averagesalary of this year’s computer science graduates is statistically-significantly higher than $50,352.Example: Auto BatteriesGrand Auto Corporation produces auto batteries. The company claims that its top-of-the-lineNever Die batteries are good, on average, for at least 65 months. A consumer protection agencytested 15 such batteries to check this claim. It found the mean life of these 15 batteries to be 63months with a standard deviation of 2 months. At the 5% significance level, can you concludethat the claim of the company is true? Assume that the life of such a battery has anapproximately normal distribution.Our hypotheses are H0: µ = 65 and H1: µ < 65. We will use the T-Test, choosing Stats, withµ0 = 65, Ë = 63, Sx = 2, n = 15, and μ1< µ0 for our alternative hypothesis.Press the STAT key.Press the ► key twice to highlight TESTS.Press the number 2 key.Move the cursor over Stats and press the ENTER key.Type in 65 for μ0.Type in 63 for X.Type in 2 for Sx.Type in 15 for n.Move the cursor over <μ0 and press the ENTER key.Move the cursor over Calculate and press the ENTER key.The T-Test output shows the alternative hypothesis: μ<65 test statistic: t=-3.872983346 p-value: p=8.4464649E-4 sample mean: X=63 sample standard deviation: Sx=2 sample size: n=15The p-value is 8.446×10−4, which is less than 5%. We reject H0 and conclude that the averagebattery lifetime is statistically-significantly less than 65 months.2Hypothesis Tests About ProportionsHypothesis tests about proportions are Z-based for sample sizes over 30. The calculator providesa function called 1-PropZTest that computes a test statistics and p-value. The 1-PropZTest islocated on the STAT page under the Tests list. The menu for 1-PropZTest is very similar to theone for 1-PropZInt described in the last chapter. Again you need to enter x, the number ofsuccesses, and n, the sample size. You also need to enter p0, the number that p is being comparedwith, and the alternative hypothesis.Example: Defective ChipsWhen working properly, a machine that is used to make chips for