The Journal de Botanique reported that the mean height of Begonias grown while being treated with a particular nutrient is 42 centimeters. To check whether this is still accurate, heights are measured for a random sample of 10 Begonias grown while being treated with the nutrient. The sample mean and sample standard deviation of those height measurements are 46 centimeters and 8 centimeters, respectively. Assume that the heights of treated Begonias are approximately normally distributed. Based on the sample, can it be concluded that the population mean height of treated begonias, μ, is different from that reported in the journal? Use the 0.05 level of significance. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. H:0 H₁:0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) (e) Can it be concluded that the mean height of treated Begonias is different from that reported in the journal? OYes ONO μ Ix ☐#0 X a S 2 On OSO Р 3 0

The size of the left upper chamber of the heart is one measure of cardiovascular health. When the upper left chamber is enlarged, the risk of heart problems is increased. A paper described a study in which the left atrial size was measured for a large number of children aged 5 to 15 years. Based on these data, the authors concluded that for healthy children, left atrial diameter was approximately normally distributed with a mean of 26.2 mm and a standard deviation of 4.1 mm. (Round your answers to four decimal places.) A USE SALT (a) Approximately what proportion of healthy children have left atrial diameters less than 24 mm? (b) Approximately what proportion of healthy children have left atrial diameters greater than 32 mm? (c) Approximately what proportion of healthy children have left atrial diameters between 25 and 30 mm? (d) For healthy children, what is the value for which only about 20% have a larger left atrial diameter? mm

A sports writer wants to see if a football filled with helium travels farther, on average, than a football filled with air. 12 footballs were filled with helium to the recommend pressure and 15 footballs were filled with air to the recommended pressure. The mean yardage for the helium filled footballs was 267 yards with a standard deviation of 3 yards. The mean yardage for the air filled footballs was 241 yards with a standard deviation of 5 yards. Assume the populations are normal with equal variances. (a). Construct a 99% confidence interval for the mean difference in in yardage for the two types of footballs Lower bound (use 3 decimal places) Upper bound (use 3 decimal places) (b). What can you conclude about the sports writer's idea that helium footballs travel farther, on average? The helium footballs are no different than the other footballs, on average The other footballs travel farther on average than the helium footballs The helium footballs travel farther on average than the…

The size of the left upper chamber of the heart is one measure of cardiovascular health. When the upper left chamber is enlarged, the risk of heart problems is increased. A paper described a study in which the left atrial size was measured for a large number of children aged 5 to 15 years. Based on these data, the authors concluded that for healthy children, left atrial diameter was approximately normally distributed with a mean of 26.1 mm and a standard deviation of 4.5 mm. (Round your answers to four decimal places.)   Approximately what proportion of healthy children have left atrial diameters less than 24 mm? Approximately what proportion of healthy children have left atrial diameters greater than 32 mm? Approximately what proportion of healthy children have left atrial diameters between 25 and 30 mm? For healthy children, what is the value for which only about 20% have a larger left atrial diameter?

A non-symmetric dataset has a mean of 200 and a standard deviation of 15.  Find an upper bound for the proportion of data points that are either greater than 230 or less than 170.

Humerus bones from the same species of animal have approximately the same length-to-width ratios. It is known that Species A has a mean ratio of 5.9. Suppose that 100 fossil humerus bones were unearthed at a site where Species A is known to have flourished. (We assume that all bones are from the same species.) The length-to-width ratios of these bones have a sample mean 5.6 and sample standard deviation 0.25.   Can we conclude that the mean ratio of these bones is significantly smaller than those of Species A? Test with a 0.01 significance level.   What is the standard error?

During the busy season, it is important for the shipping manager at ShipMundo to be able to estimate the time it takes the loading crew to load a truck. The shipping manager has found that she can model the load times using a normal distribution with a mean of 152 minutes and a standard deviation of 15 minutes. Use this table or the ALEKS calculator to find the percentage of load times between 116 minutes and 149 minutes according to the model. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example 98.23%).