2.A tensile strength of fiber used in a cloth manufacturing process is of interest to the purchaser. Previous experience indicated that the standard deviation of tensile strength is 2 psi. A random sample of eight fiber specimens is selected and the average tensile strength was found to 127 psi. (a) Test the hypothesis that the mean tensile strength equal 125 psi versus the alternative hypothesis that the mean exceeds 125 psi at a level of significance of 0.05. (b) What is the P-value of this test? (c) Why do you think that one sided alternative is better in this case?

The mean score in miss smiths 4th grade class was 76, with a standard deviation of 7. Assume the grades are normally distributed  and use the empirical rule to find the approximate percentage of students who scored above 83.

Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.4 and the sample standard deviation was 1.2. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value? (Use a = 0.05.) State the appropriate hypotheses. O H,: H 48 H:u = 48 O H,: = 48 Hi u 48 OH:= 48 H: u + 48 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) P-value = What can you conclude? O The data provides compelling…

Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.3 and the sample standard deviation was 1.4. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value? (Use α = 0.05.) State the appropriate hypotheses. ⒸH₂: μ = 48 Ha: > 48 Ho:μ = 48 H₂H 48 H₂: μ = 48 Ho: μ< 48 H₂₁:μ = 48 USE SALT Ho: M = 48 H₂:48 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t= 7.68 X P-value =

Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.4 and the sample standard deviation was 1.5. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value? (Use α = 0.05.) Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t  =    P-value  =

Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.1 and the sample standard deviation was 1.3. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value? (Use α = 0.05.) USE SALT State the appropriate hypotheses. ⒸHO: μ> 48 H₂: μ = 48 Ho: μ 48 Ho: μ = 48 H₂: μ = 48 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value = What can you conclude? O The data provides compelling…

Steel used for water pipelines is often coated on the inside with cement mortar to prevent corrosion. In a study of the mortar coatings of the pipeline used in a water transmission project in California, researchers noted that the mortar thickness was specified to be 7/16 inch. A very large sample of thickness measurements produced a mean equal to 0.635 inch and a standard deviation equal to 0.082 inch. If the thickness measurements were normally distributed, approximately what proportion were less than 7/16 inch?

Cans of LaCroix are supposed to contain 355 milliliters (ml). There is some variation for each can because the filling machinery is not perfectly precise. An inspector measures the contents (in ml) of 12 randomly selected cans from a single day's production. x = 352.9 Sx=2.19 Do these data provide convincing evidence at the a = 0.01 significance level that the mean amount of LaCroix in all the cans filled that day is less than the target value of 355 ml? (6pt) STATE: State hypotheses, parameters), significance level, and evidence for Ha Parameter: Statistic: Hypotheses: Significance level: Evidence for Ha: (mean less than sample) (2pt) PLAN: Identify the appropriate inference method and check conditions. Name of procedure: Check conditions: Random Sample: Normal / Large Sample: Describe what is shown.

A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with ² = 1000 (psi)². A random sample of 12 specimens has a mean compressive strength of x= 3250 psi. What must be the P-value in testing the hypothesis that u = 3225 psi against the alternative hypothesis, > 3225 psi?

A pharmaceutical manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The force in kilograms (kg) applied to the tablet varies a bit and follows the Normal distribution with mean 11.5 kg and standard deviation 0.2 kg. The process specifications call for applying a force between 11.2 and 12.2 kg. 1. Calculate the 25th percentile (P25) and the 75th percentile (P75) of the distribution. 2. ) Suppose the lifetime of a human has an expectation of 72 and variance 36. What is the probability that the average of the lifetime of 100 people exceeds 73?