The mean time to retrieve a record from an online database is 222 milliseconds with a standard deviation of 62 milliseconds. The design criterion requires that at least 80% of all retrieval times must not differ from the mean by more than 83 milliseconds. Use Chebyshev's inequality to establish whether the design criterion is satisfied. Would the design criterion be satisfied if it were known that the retrieval time is normally distributed with a mean of 222 milliseconds
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The
- Use Chebyshev's inequality to establish whether the design criterion is satisfied.
-
Would the design criterion be satisfied if it were known that the retrieval time is
normally distributed with a mean of 222 milliseconds and a standard deviation of 62 milliseconds?
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- Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 25 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.11 oz, and they appear to be from a normally distributed population. If the workers want the filling process to work so that almost all cans have volumes between 11.97 oz and 12.65 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.17 oz.Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.17 oz. Use a 0.05 significance level. Complete parts (a) through (d) below, a. Identify the null and alternative hypotheses. Choose the correct answer below. O B. Ho o=0.17 oz H, o0.17 oz H, 0 0.17 oz H o= 0.17 oz b. Compute the test statistic. (Round to three decimal places as needed.)A manufacturer claims that the mean lifetime, μ , of its light bulbs is 50 months. The standard deviation of these lifetimes is 7 months. One hundred fifty bulbs are selected at random, and their mean lifetime is found to be 51 months. Can we conclude, at the 0.05 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 50 months? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H0? and the alternative hypothesis H1? . H0: H1: (b) Determine the type of test statistic to use. ▼(Choose one) z ? t ? chi square? f? (c) Find the value of the test statistic.? (Round to three or more decimal places.) (d) Find the two critical values.? (Round to three or more decimal places.) and…Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 21 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.11 oz, and they appear to be from a normally distributed population. If the workers want the filling process to work so that almost all cans have volumes between 11.91 oz and 12.47 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.14 oz. Use the sample data Complete parts (a) through (d) below. test the claim that the population of volumes has a standard deviation less than 0.14 oz. Use a 0.025 significance level. a. Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho: o = 0.14 oz O B. Ho: o = 0.14 oz H,:o0.14 oz H1: 0 = 0.14 oz O D. Ho: o20.14 oz H:o<0.14 oz b. Compute the test statistic. (Round to three decimal places as needed.) c. Find the P-value. P-value = (Round to four decimal places as…
- A newspaper article reported that people spend a mean of 6.5 hours per day watching TV, with a standard deviation of 1.9 hours. A psychologist would like to conduct interviews with the 10% of the population who spend the most time watching TV. She assumes that the daily time people spend watching TV is normally distributed. At least how many hours of daily TV watching are necessary for a person to be eligible for the interview? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place. hoursA manufacturer claims that the mean lifetime, u, of its light bulbs is 44 months. The standard deviation of these lifetimes is 7 months. Twenty-three bulbs are selected at random, and their mean lifetime is found to be 48 months. Assume that the population is normally distributed. Can we conclude, at the 0.01 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 44 months? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. p H, :0 H, :0 (b) Determine the type of test statistic to use. (Choose one) v O=0 OSO |(c) Find the value of the test statistic. (Round to three or more decimal places.) OA newspaper article reported that people spends a mean of 6 hours per day watching tv, with a standard deviation of 1.8 hours. A psychologist would like to conduct interviews with the 15% of the population who spend the most time watching tv. She assumes that the daily time spent watching tv is normally distributed. At least how many hours of daily tv watching are necessary to be eligible for the interview? Carry intermediate computations to 4 places, and the answer to 1.A bottler carefully weighs bottles coming off its production line to check that the system is filling the bottles with the correct amount of beverage. By design, the system is set to slightly overfill the bottles to allow for random variation in the packaging. The content weight is designed to be 814 g with standard deviation 9 g. Complete parts (a) and (b) below. (a) A proposed system shuts down the facility if the contents of a bottle weigh less than 800 g. What is the chance of a Type I error with this system? The chance of a Type I error is (Round to four decimal places as needed.)A manufacturer claims that the mean lifetime, u, of its light bulbs is 42 months. The standard deviation of these lifetimes is 6 months. Twenty-seven bulbs are selected at random, and their mean lifetime is found to be 41 months. Assume that the population is normally distributed. Can we conclude, at the 0.01 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 42 months? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H1. p H, :0 H, :0 (b) Determine the type of test statistic to use. D=D OSO (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values. (Round to three or more decimal places.) Dand (e) Can we conclude that the mean lifetime of…The brain volumes (cm cubed) of 20 brains have a mean of 1119.1 cm cubed and a standard deviation of 121.7 cm cubed. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such data, would a brain volume of 1382.5 cm cubed be significantly high?Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 24 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.12 oz, and they appear to be from a normally distributed population. If the workers want the filling process to work so that almost all cans have volumes between 11.94 oz and 12.46 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.13 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.13 oz. Use a 0.05 significance level. Complete parts (a) through (d) below. a. Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho: o = 0.13 oz O B. Ho: o = 0.13 oz H1: o+0.13 oz H1: o 0.13 oz H1: 0 = 0.13 oz O D. Ho: o20.13 oz H1: o<0.13 oz b. Compute the test statistic. x2 = 19.598 (Round to three decimal places as needed.) c. Find the P-value. P-value =…A manufacturer claims that the mean lifetime, μ , of its light bulbs is 55 months. The standard deviation of these lifetimes is 6 months. Forty-two bulbs are selected at random, and their mean lifetime is found to be 58 months. Assume that the population is normally distributed. Can we conclude, at the 0.05 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 55 months? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic:(Round to at least three decimal places.) The two critical values at the 0.05 level of significance:(Round to at least three decimal places.) and Can we…