Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 19 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.14 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 11.86 oz and 12.54 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 0.025 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: o<0.17 oz O A. Ho: 020.17 oz H, o<0.17 oz O D. Ho: o= 0.17 oz O C. Ho o>0.17 oz H,: o=0.17 oz H,: o#0.17 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 needed.) d. State the conclusion. Do not reject Ho, because the P-value is less than or equal to the level of significance. There is insufficient evidence to conclude that the population standard deviation of can volumes is less than 0.17 oz.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 19 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.14 oz, and they appear to be from a
Identify the null and alternative hypotheses. Choose the correct answer below.
Compute the test statistic.
Find the P-value.
State the conclusion.
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