On average, a car battery lifespan in Malaysia ranges from two to five years. It could be affected by the battery brand, vehicle type, area's climate, car care, and driving pattems. A researcher is interested to compare the car battery lifespan between two types of brands. The statistics of two brands of batteries are given in the following table. Brand A Brand B Sample mean Sample variance Sample size 2.8 3.1 1.2 1.5 10 12 Assume that the populations are approximately normally distributed. a) Construct a 90% confidence interval for the ratio of two variances of battery lifespan between Brand A and Brand B. Identify whether the two variances are equal or unequal.

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c)
A manufacturer of Brand A claims that their battery will last more than 2.5 years. Test at
5% significance level to support the claims.
Transcribed Image Text:c) A manufacturer of Brand A claims that their battery will last more than 2.5 years. Test at 5% significance level to support the claims.
On average, a car battery lifespan in Malaysia ranges from two to five years. It could be
affected by the battery brand, vehicle type, area's climate, car care, and driving pattems. A
researcher is interested to compare the car battery lifespan between two types of brands.
The statistics of two brands of batteries are given in the following table.
Brand A
Brand B
Sample mean
Sample variance
Sample size
2.8
3.1
1.2
1.5
10
12
Assume that the populations are approximately normally distributed.
a) Construct a 90% confidence interval for the ratio of two variances of battery lifespan
between Brand A and Brand B. Identify whether the two variances are equal or unequal.
b) Based on your answer in a), test at 5% significance level whether there is a significant
difference on the mean lifespan between Brand A and Brand B.
Transcribed Image Text:On average, a car battery lifespan in Malaysia ranges from two to five years. It could be affected by the battery brand, vehicle type, area's climate, car care, and driving pattems. A researcher is interested to compare the car battery lifespan between two types of brands. The statistics of two brands of batteries are given in the following table. Brand A Brand B Sample mean Sample variance Sample size 2.8 3.1 1.2 1.5 10 12 Assume that the populations are approximately normally distributed. a) Construct a 90% confidence interval for the ratio of two variances of battery lifespan between Brand A and Brand B. Identify whether the two variances are equal or unequal. b) Based on your answer in a), test at 5% significance level whether there is a significant difference on the mean lifespan between Brand A and Brand B.
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