To answer this question, we can use a hypothesis test. Our null hypothesis is that the standard deviation of the battery lifespans is indeed 1 year, and our alternative hypothesis is that it is not.

We can use a chi-square test to test this hypothesis. The test statistic is:

χ2 = (n-1) * s2 / σ2

where n is the sample size, s is the sample standard deviation, and σ is the population standard deviation (which we are testing).

Plugging in the values from the problem, we get:

χ2 = (5-1) * 1.23 / 12 = 0.41

Using a chi-square distribution table with 4 degrees of freedom (since we have 5 data points and are estimating 1 parameter), we find that the critical value for a 95% confidence level is 9.49.

Since our test statistic (0.41) is much smaller than the critical value (9.49), we fail to reject the null hypothesis. This means that there is not enough evidence to suggest that the standard deviation of the battery lifespans is different from 1 year. Therefore, the manufacturer can still be confident in their claim.