A bearing used in an automotive application is required to have a nominal inside diameter of 1.5 inches. A random sample of 25 bearings is selected and the average inside diameter of these bearings is 1.4975 inches. Bearing diameter is known to be normally distributed with standard deviation o = 0.01 inch. (a) Test the hypotheses Ho: μ = 1.5 versus H₁ : μ The true mean hole diameter (b) What is the P-value for the test in part (a)? P-value = i 1.5 using a = 0.01. significantly different from 1.5 in. at a = 0.01. (c) Compute the power of the test if the true mean diameter is 1.495 inches. Power of the test = i Round your answer to two decimal places (e.g. 98.76). bearings (d) What sample size would be required to detect a true mean diameter as low as 1.495 inches if we wanted the power of the test to be at least 0.90? Round your answer to two decimal places (e.g. 98.76). Statistical Tables and Charts

A student made three measurements of the mass of an object using a balance (± 0.01 g) and obtained the following values: Measure # 1 4.39 ± 0.01 g Measure # 2 4.42 ± 0.01 g Measure # 3 4.41 ± 0.01 g   Find the mean value and its standard deviation and express the result to the correct significant figures.   Choose one   A) (4.41 ± 0.02) g B) (4.40 ± 0.01) g C) (4.40 ± 0.02) g D) (4.406 ± 0.0152) g

The slant shear test is widely accepted for evaluating the bond of resinous repair materials to concrete; it utilizes cylinder specimens made of two identical halves bonded at 30°. An article reported that for 12 specimens prepared using wire-brushing, the sample mean shear strength (N/mm2) and sample standard deviation were 18.60 and 1.56, respectively, whereas for 12 hand-chiseled specimens, the corresponding values were 23.19 and 4.07. Does the true average strength appear to be different for the two methods of surface preparation?   State and test the relevant hypotheses using a significance level of 0.05. (Use ?1 for wire-brushing and ?2 for hand-chiseling.) H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≤ 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 < 0    H0: ?1 − ?2 = 0Ha: ?1 − ?2 > 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≠ 0 Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.) t  =    P-value  =   You may have computed…

The mean body mass index (BMI) for boys age 12 is 23.6. An investigator wants to test if the BMI is higher in 12-year-old boys living in New York City.  How many boys are needed to ensure that a two-sided test of hypothesis has 80% power to detect a difference in BMI of 2 units?  Assume that the standard deviation in BMI is 5.7.     Alpha = ________     Z1-α/2= ________      Z1-β = ________        ES = ________           n= ________