question 1

A somewhat outdated study indicates that the mean number of hours worked per week by software developers is $4. We have good reason to suspect that the mean number of hours worked per week by software developers, p. is now different from 44 and wish to do a statistical test. We select a random sample of software developers and find that the mean of the sample is 47 hours and that the standard deviation is 4 hours. Based on this information, complete the parts below. () what are the null hypothesis My and the alternative hypothesis H, that should be used for the test? 0 0 010 0 0 (b) Suppose that we decide not to reject the null hypothesis. What sort of error might we be making? (Choose one) X 5 2 Type I Type II(C) Suppose the true mean number of hours worked by software engineers is 44 hours. Fill in the blanks to describe a Type I error. rejecting failing to reject the hypothesis that u is (Choose one) less than less than or equal to greater than greater than or equal to not equal to equal to 47 44 when, in fact, u is (Choose one) equal to 44 equal to 4 equal to 47 not equal to 44 less than 4 greater than 47The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.8 auto accidents per day with a standard deviation of 0.04. The actuaries of the company claim that the standard deviation of the number of accidents per day is no longer equal to 0.04. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis , and the alternative hypothesis , that we would use for this test. Ho: H X p H: 1 P S OSO >0 020 0=0 0#0An independent consumer group published its finding that the lifetimes of electric bulbs manufactured by BIG Corporation are approximately normally distributed with a mean of 600 days and a variance of 14,762.25. BIG Corporation claims that the variance of its electric bulbs is less than 14,762.25. Suppose that we want to carry out a hypothesis test to see if BIG Corporation's claim is correct. State the null hypothesis Ho and the alternative hypothesis H, that we would use for this test. H X P H : 1 O S 00 020 0=0 0#0The human resources department of a large investment bank announced that the number of people it interviews monthly has a mean of 115 with a standard deviation of 16.7. The management of the bank suspects that the standard deviation exceeds 16.7. Suppose that the management wants to take a small sample of months and carry out a hypothesis test to see if its suspicions have support. State the null hypothesis #, and the alternative hypothesis H, that it would use for this test. Ho: X p H1 : 1 p S 00 020 0=0 0#0(c) Find the value of the test statistic. (Round to three or more decimal places.) ? (d) Find the p-value. (Round to three or more decimal places.) X (e) Can we support the claim that the population mean completion time under new management is less than 12.3 minutes? OYes ONoBefore changes to its management staff, an automobile assembly line operation had a scheduled mean completion time of 12 3 minutes. The standard deviation of completion times was 1.7 minutes. An analyst at the company suspects that, under new management, the mean completion time, j, is now less than 12.3 minutes. To test this claim, a random sample of 23 completion times under new management was taken by the analyst. The sample had a mean of 11.4 minutes. Assume that the population is normally distributed. Can we support, at the 0.01 level of significance, the claim that the population mean completion time under new management is less than 12.3 minutes? Assume that the population standard deviation of completion times has not changed under new management. Perform a one-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 Ho and the alternative hypothesis H. H HQ :0 5 [b] Determine the type of test statistic to use. (Choose one) 0-0 050 020 Degrees of freedom: Chi-square Degrees of freedom: F Degrees of freedom: din: dfd :The breaking strengths of cables produced by a certain manufacturer have historically had a mean of 1825 pounds and a stand: company believes that, due to an improvement in the manufacturing process, the mean breaking strength, j, of the cables is n see if this is the case, 17 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is four that the population is normally distributed. Can we support, at the 0.05 level of significance, the claim that the population mear manufactured cables is greater than 1825 pounds? Assume that the population standard deviation has not changed. Perform a one-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 necess (a) State the null hypothesis Ho and the alternative hypothesis H. O Ho : 0 S H :0 (b) Determine the type of test statistic to use. (Choose one) 0=0 030 020 0*0 00 Degrees of freedom: Z Chi-square Degrees of freedom: F Degrees of freedom: din: 0 did: ]The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.9 auto accidents per day with a variance of 0.0036. The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0036. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis #, and the alternative hypothesis #, that we would use for this test. Ho: X p H : I S 00 020 0=0 0#0{c} Find the 1iralue of the test statistic. {Round to three or more decimal places.) D {d} Find the pvalue. [Round to three or more decimal places.) D {e} lCan we support the claim that the population mean breaking strength of the newlymanufactured cables is greater than 1325 pounds? Gites C} No According to a report done by S & J Power, the mean lifetime of the light bulbs it manufactures is 42 months. A researcher for a consumer advocate group tests this by selecting 27 bulbs at random. For the bulbs in the sample, the mean Wifetime is 43 months. It is known that the population standard deviation of the lifetimes is 9 months. Assume that the population is normally distributed. Can we conclude, at the 0.10 level of significance, that the population mean lifetime. in. 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 Ho and the alternative hypothesis H. Ho : 0 H :0 (b) Determine the type of test statistic to use. (Choose one) Degrees of freedom: Z Chi-square Degrees of freedom: F Degrees of freedom: din: [ did: 0 |0-0 050 020 DO 0