The sugar content of the syrup in canned peaches is normally distributed. A random sample of n = 10 cans yields a sample standard deviation of s = 4.8 milligrams. Calculate a 95% two-sided confidence interval for σ.

The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.37. Construct a 95% two-sided confidence interval σ.

The 2004 presidential election exit polls from the critical state of Ohio provided the following results. The exit polls had 2020 respondents, 768 of whom were college graduates. Of the college graduates, 412 voted for George Bush. a. Calculate a 95% confidence interval for the proportion of college graduates in Ohio who voted for George Bush. b. Calculate a 95% lower confidence bound for the proportion of college graduates in Ohio who voted for George Bush.

A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with $σ^2 = 1000\textrm{psi}^2$. A random sample of 12 specimens has a mean compressive strength of $\overline{x}=3250\textrm{psi}$.

a. Construct a 95% two-sided confidence interval on mean compressive strength.

b. Construct a 99% two-sided confidence interval on mean compressive strength. Compare the width of this confidence interval with the width of the one found in part (a).

Determine the values of the following percentiles: X²0.05,10, X²0.025,15, X²0.01,12, X²0.95,20, X²0.99,18, X²0.995,16, and X²0.005, 25.

The wall thickness of 25 glass 2-liter bottles was measured by a quality-control engineer. The sample mean was $\overline{x}=4.058 \mathrm{mm},$ and the sample standard deviation was s = 0.081 mm. (a) Suppose that it is important to demonstrate that the wall thickness exceeds 4.0 mm. Formulate and test appropriate hypotheses using these data. Draw conclusions at $\alpha = 0.05.$ Calculate the P-value for this test. (b) Find a 95% lower confidence bound for mean wall thickness. Interpret the interval you obtain.

A research engineer for a tire manufacturer is investigating tire life for a new rubber compound and has built 16 tires and tested them to end-of-life in a road test. The sample mean and standard deviation are 60,139.7 and 3645.94 kilometers. Find a 95% confidence interval on mean tire life.

The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.37. (a) Test the hypothesis $H_{0} : \sigma=0.35 \text { versus } H_{1} : \sigma \neq 0.35$ using $\alpha = 0.05.$ State any necessary assumptions about the underlying distribution of the data. (b) Find the P-value for this test. (c) Construct a 95% two-sided CI for $\sigma.$ (d) Use the CI in part (c) to test the hypothesis.

The yield of a chemical process is being studied. From previous experience, yield is known to be normally distributed and σ = 3. The past five days of plant operation have resulted in the following percent yields: 91.6, 88.75, 90.8, 89.95, and 91.3. Find a 95% two-sided confidence interval on the true mean yield.

An article in Knee Surgury, Sports Traumatology, Arthroscopy (“Arthroscopic Meniscal Repair with an Absorbable Screw: Results and Surgical Technique,” 2005, Vol. 13) showed that 25 out of 37 tears located between 3 and 6 mm from the meniscus rim were healed. (a) Calculate a two-sided traditional CI on the proportion of such tears that will heal. (b) Calculate a 95% one-sided traditional confidence bound on the proportion of such tears that will heal.

Information on a packet of seeds claims that 93% of them will germinate. Of the 200 seeds that I planted, only 180 germinated. a. Find a 95% confidence interval for the true proportion of seeds that germinate based on this sample. b. Does this seem to provide evidence that the claim is wrong?

Determine the

$$X_2$$

percentile that is required to construct each of the following CIs: a. Confidence level = 95%, degrees of freedom = 24, one sided (upper) b. Confidence level = 99%, degrees of freedom = 9, one-sided (lower) c. Confi dence level = 90%, degrees of freedom = 19, two-sided.

A random sample of 50 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test, and on 18 of these helmets some damage was observed. (a) Test the hypotheses $H_0: p = 0.3$ versus $H_{1} : p \neq 0.3$ with $\alpha = 0.05.$ (b) Find the P-value for this test. (c) Find a 95% two-sided traditional CI on the true proportion of helmets of this type that would show damage from this test. Explain how this confidence interval can be used to test the hypothesis in part (a). (d) Using the point estimate of p obtained from the preliminary sample of 50 helmets, how many helmets must be tested to be 95% confident that the error in estimating the true value of p is less than 0.02? (e) How large must the sample be if we wish to be at least 95% confident that the error in estimating p is less than 0.02, regardless of the true value of p?

Recall the sugar content of the syrup in canned peaches. Suppose that the variance is thought to be $\sigma^{2}=18$(milligrams)$^{2}$. A random sample of n = 10 cans yields a sample standard deviation of s = 4.8 milligrams. (a) Test the hypothesis $H_{0}: \sigma^{2}=18$ versus $H_{1}: \sigma^{2} \neq 18$ using $\alpha=0.05$. (b) What is the P-value for this test? (c) Discuss how part (a) could be answered by constructing a 95% two-sided confidence interval for $\sigma$.