degradation. A company producing automobile batteries is developing a prototype on their next product and that they claim their batteries will last on average, 3 years with a variance of 1 year. A random sample of 5 prototype batteries were taken and in the course of the company's product development, have measured their lifetimes as 1.9, 2.4, 3.0, 3.5, and 4.2 years. Construct a 95% confidence interval for o and decide if the company's claim that o? = 1 is valid. Assume the population of battery lives to be approximately normally distributed. Da. 0.29 < o2 < 6.74. Because 95% confidence interval for o? is (0.29, 6.74), and 1 is in that interval, we can conclude that the company's claim that o? = 1 is valid %3D O b. 0.539 < o < 2.596. Because 95% confidence interval for o is (0.539, 2.596), and 1 is in that interval, we can conclude that the company's claim that o = 1 is valid Oc. 0.34 < o2 < 4.59. Because 95% confidence interval for o? is (0.34, 4.59), and the s2 is in that interval, we can conclude that the company's claim is valid = 0.815 ) d. 0.29 < o2 < 6.74. 95% confidence interval for o2 is (0.29, 6.74)

Find the 90% confidence interval for the difference in the means.

The quality control manager of a car antifreeze manufacturer wants to find the fluctuations in the amount of antifreeze solution that a container can hold.  She selects a sample of 18 such container and arrives at an average of 3787 lb., and a s.  d. of 55.4 lb.   Using this sample data construct a 95% confidence interval for the standard deviation of the car antifreeze.

You work for a company that produces electronics with integrated circuits. One of your products is called a "shift register." This product is designed to automatically shut down if its operating temperature exceeds 175 degrees Celsius. The manufacturing process has been designed to have a standard deviation of o = 0.4 degrees Celsius. You test a random sample 19 shift registers, and you record the following shut- down temperatures. Construct a 90% confidence interval for the overall mean shutdown-temperature. 175 174.66 175.44 174.34 174.91 174.79 174.82 175.52 174.99 174.99 175.23 175.15 175.11 175 175.43 174.85 174.74 174.9 175.48 (Checksum: 3325.35) a) Find the critical value and o. Critical Value: b) Find the confidence interval: 100% " 70°F Cloudy

You work for a company that produces electronics with integrated circuits.  One of your products is called a "shift register."  This product is designed to automatically shut down if its operating temperature exceeds 175 degrees Celsius.  The manufacturing process has been designed to have a standard deviation of σ=0.4σ=0.4 degrees Celsius.  You test a random sample 16 shift registers, and you record the following shut-down temperatures. Construct a 80% confidence interval for the overall mean shutdown-temperature.   175.61 175.44 175.24 175.49 174.57 175.44 174.67 175.72 175.3 175.65 174.83 175.29 175.13 175.05 174.74 174.8     (Sum of data values = 2802.97) a) Find the critical value and σ¯xσx¯ . Round your answers to 3 decimal places. Critical Value:      σ¯xσx¯ :  b)  Find the confidence interval, rounded to 2 decimal places:  (,)

You work for a company that produces electronics with integrated circuits. One of your products is called a "shift register." This product is designed to automatically shut down if its operating temperature exceeds 175 degrees Celsius. The manufacturing process has been designed to have a standard deviation of o = 0.4 degrees Celsius. You test a random sample 20 shift registers, and you record the following shut- down temperatures. Construct a 98% confidence interval for the overall mean shutdown-temperature. 175.14 174.25 175.18 175.59 174.93 175.56 174.46 174.6 174.83 175.2 174.87 174.14 174.51 174.52 175.46 175.11 175.24 175.05 174.97 174.4 (Checksum: 3498.01) a) Find the critical value and oã . Critical Value: b) Find the confidence interval:

A school district decided to measure the BMI of all 3rd graders and identify the highest 1% and lowest 1% of those students. If the distribution is converted to a z distribution, what would be the upper critical z value and lower critical z value that mark the two significant areas at the tails?

Hoaglin, Mosteller, and Tukey (1983) presented data on blood levels of beta-endorphin as a function of stress. They took beta-endorphin levels for 19 patients 12 hours before surgery and again 10 minutes before surgery.  The data are presented below, in fmol/ml Construct a 95% confidence limits on the true mean difference between endorphin levels at the two times described.    Participant                   12 hours before           10 minutes before 1                                  10                                6.5 2                                  6.5                               14.0 3                                  8.0                               13.5 4                                  12                                18 5                                  5.0                               14.5 6                                  11.5                             9.0 7                                  5.0                               18.0 8…

You work for a company that produces electronics with integrated circuits. One of your products is called a "shift register." This product is designed to automatically shut down if its operating temperature exceeds 175 degrees Celsius. The manufacturing process has been designed to have a standard deviation of o = 0.4 degrees Celsius. You test a random sample 16 shift registers, and you record the following shut- down temperatures. Construct a 80% confidence interval for the overall mean shutdown-temperature. 174.99 174.76 174.99 174.61 174.86 174.41 175.54 174.13 174.96 174.78 174.84 174.67 174.87 175.52 174.88 175.35 (Checksum: 2798.16) a) Find the critical value and ₂. Critical Value: σz: b) Find the confidence interval:

Age x and resting heart rate y were sampled for 25 randomly selected children from age 2 to 9. Summary information is:  n = 25, Σx = 140.5, Σx2 = 903.75, Σy = 2567, Σy2 = 264, 457, Σxy = 14, 171.5 (a) Compute a 95% confidence interval for the average resting heart rate of 3 six year old children.