Do Consumer Group Have Evidence to Dispute Manufacturer's Claim?

Do the consumer group have sufficient evidence to dispute the manufacturer's claim that their batteries have a mean life of 60 months?

No, at the 0.05 significance level, the consumer group does not have sufficient evidence to dispute the manufacturer's claim regarding the mean battery life.

Analysis of Consumer Group's Data

The Consumer Group's Hypotheses: The consumer group is trying to determine if the mean battery life of 60 months claimed by the manufacturer can be disputed based on their sample of 30 batteries with a mean lifetime of 58.5 months and a known standard deviation of 6.5 months.

Statistical Testing:

The consumer group can use a one-sample t-test since the population standard deviation is known. The null hypothesis (H0) assumes that the batteries do have a mean lifetime of 60 months, while the alternative hypothesis (H1) assumes that the batteries do not have a mean lifetime of 60 months.

Calculation of t-Value:

The formula for the t-test statistic is given by: t = (Sample Mean - Population Mean) / (Population Standard Deviation / √Sample Size)

Plugging in the values gives a calculated t-value of approximately -1.938.

Conclusion:

Since the calculated t-value (-1.938) is less than the critical t-value (-2.045) at the 0.05 significance level with 29 degrees of freedom, the consumer group fails to reject the null hypothesis. Therefore, there is not enough evidence to dispute the manufacturer's claim of a mean battery life of 60 months.

In conclusion, the consumer group's analysis does not provide sufficient evidence to dispute the manufacturer's claim at the 0.05 significance level. The sample mean of 58.5 months is not significantly different from the claimed mean life of 60 months.