Question

A manufacturing firm claims that the batteries

used in their electronic games will last an average of

30 hours. To maintain this average, 16 batteries are

tested each month. If the computed t-value falls between

?t0.025 and t0.025, the firm is satisfied with its

claim. What conclusion should the firm draw from a

sample that has a mean of x = 27.5 hours and a standard

deviation of s = 5 hours? Assume the distribution

of battery lives to be approximately normal.

Answer 1

To assess the manufacturing firm's claim about battery life, we calculate a t-value using the sample mean, standard deviation, and size. If the t-value falls within the critical value range, the claim about a 30-hour average battery life is supported.

Step-by-step explanation:

The scenario described involves a statistical test regarding the average lifespan of batteries produced by a manufacturing firm. To determine if the firm's claim about the battery life is valid, we use the computed t-value from the sample data. This involves comparing the sample mean to the population mean under the assumption of the population's normal distribution, with a given sample standard deviation and size.

In this case, we would calculate the observed t-value by subtracting the expected battery life from the sample mean, then dividing by the standard error (the sample standard deviation divided by the square root of the sample size). If this calculated t-value falls within the critical t-values at the 0.025 level on both tails of the distribution (±t0.025), the firm can be confident in their claim about the battery life. Otherwise, the firm may need to review their production process or the validity of their claim.