Batteries R Us is a manufacturer of batteries and are testing a new production technique for their most popular battery type. It is known that the mean lifetime of these batteries made using the previous production technique was 65 hours. The standard deviation in battery lifetime is 5.6 hours and it is assumed that this has not changed. They would like to know whether mean battery lifetime has increased with the new production technique.

The following sample data of battery lifetimes has been collected from a random sample of 40 batteries made using the new manufacturing technique.

68.5

58.6

68

67.5

66.8

61.2

56.4

67.9

66

65.2

72.1

74.2

62.8

66.6

62.8

66.6

64.8

80.8

72.6

69.7

61.5

63.4

79

51.1

64

73.7

65.5

63

70.7

73.2

70.7

60.3

63.4

65

63.3

69.8

71.8

65.3

64.8

56.9

Conduct a hypothesis test to test whether the new manufacturing process has increased mean battery lifetime.

a)From the following options, select the correct null and alternate hypotheses for this test:

A:H₀: = 65, H_a: 65

B:H₀: > 65, H_a: = 65

C:H₀: = 65, H_a: > 65

D:H₀: = 65, H_a: < 65

The correct null and alternate hypotheses for this test are:

A

B

C

D

b)Calculate the test statistic. Give your answer to 2 decimal places.

z =

c)Calculate the p-value for the test. Give your answer to 4 decimal places.

P-value =

d)Therefore, at a significance level of 0.05 the null hypothesis is

• rejected
• not rejected

e)At a significance level of 0.05, from the result of the test you can conclude that there is:

A. proof

B.significant evidence

C.not enough evidence

to conclude that the

A.population mean battery lifetime

B.sample mean battery lifetime

has

A.increased

B.decreased

C.not changed

.