Following is a problem description. For all hypothesis tests, you MUST show all 7 steps we have been using and use the P-VALUE METHOD to make your decision.For confidence intervals, there are not specific steps, but there is a specific Excel tool for each interval.They should not be done by-hand for this set, nor should you simply use Excel formulas to use it as a calculator.Treat each question as a separate problem -- we use the same data set, but are answering different "research questions". You must attach and clearly label the Excel output that you use in answering the questions as appropriate. The part of the printout you are using must be clearly identified.

Videocassette recorder (VCR) tapes are designed so that users can repeatedly record new material over old material. However, after a number of re-recordings the tape begins to deteriorate. A VCR tape manufacturer is experimenting with a new technology, which hopefully will produce longer-lasting tapes. Thirty of the old-style tapes and 30 utilizing the new technology were used in an experiment. The tapes were used to record and rerecord programs until they began to deteriorate. The number of re-recordings were observed and shown in the accompanying table.It is generally accepted that the number of re-recordings should exceed 55. Any that do not are considered unacceptable.(NOTE:This does not mean you throw them out! They are part of the sample, and we expect some to be unacceptable ... that is why we are testing!)The number of re-recordings is assumed to be normally distributed.

NOTE: use ONLY the P-value method for hypothesis tests. If you include both rules in step 4 or include both in your decision step, I will have to conclude that you do not yet understand the p-value rule.

Old-Style Tapes

60

61

48

51

46

66

66

63

61

73

55

71

71

49

76

47

56

55

60

62

64

52

51

63

64

68

52

47

55

58

New Technology Tapes

68

70

58

74

72

69

77

73

49

59

66

61

52

58

59

66

51

49

62

59

57

51

56

66

50

55

76

63

68

78

Answer the following four questions:

a.) Can we conclude at the 10% significance level that the mean number of re-recordings of the new tapes is greater than 55?

b) Estimate with 90% confidence the difference in the mean number of re-recordings between the old and new tapes and interpret the interval.

c.) Can we infer at the 10% significance level that the variance of the number of re-recordings of the new tape is less than 100?

d.)The quality control manager is not only concerned about the number of re-recordings but is also concerned about the proportion of unacceptable tapes.Do the data allow us to infer at the 10% significance level that the new technology tapes are superior to the old-style tapes in terms of the proportion of unacceptable tapes?