Colonial Funds claims to have a bond fund that has maintained a mean share price of $⁢10.00. They claim that the variance of the share price is 0.18. To test this claim, the investor randomly selects 29 days during the last year. He finds an average share price of $⁢9.80 with a standard deviation of 0.4006. Can the investor conclude that the share price of the bond fund varies from Colonial Funds claims at α=0.05? Step 1 of 5 : State of the hypotheses in terms of the standard deviation. Round the standard deviation to four decimal places when necessary Step 2 of 5 : Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places. Step 3 of 5 : Determine the value of the test statistic. Round your answer to three decimal places. Step 4 of 5 : Make the decision. Step 5 of 5 : What is the conclusion?

From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant at around 2.1 years. A survey of 41 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.2 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level? Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part 1) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value Part 2) Alpha (Enter an exact number as an integer, fraction, or decimal.)α =  Part 3) Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper…

From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant at around 2.1 years. A survey of 42 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level?Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)     State the distribution to use for the test. (Round your answers to four decimal places.) X  ~         ,     What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)     =  What is the p-value? (Round your answer to four decimal places.)

The Credit Risk Department of a major bank estimates the default rate on loans under $10,000 to be 4%. The bank will make 2400 loans that are under $10,000 next month. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p, where p is the proportion of defaults on the 2400 loans under $10,000 to be made next month. (b) Find the standard deviation of p. (c) Compute an approximation for P(p 2 0.03), which is the probability that 3% or more of next month's loans under $10,000 will be defaulted on. Round your answer to four decimal places.