Fizzco, a beverage manufacturing company, is interested in determining whether the standard deviation of their dispensing process has changed from a required level of 5 milliliters. They have taken a random sample of 12 bottles and have measured the amount of beverage dispensed into each bottle (in milliliters) as shown below:
352 345 347 357 341 356
349 343 346 351 348 361
a. Calculate the point estimate of σ.
b. Construct the 95% confidence interval for the population standard deviation. Assume the amount of beverage dispensed follows a normal distribution.
c. At the 5% significance level, can we conclude that the standard deviation of the amount of beverage dispensed differs from the required level of 5 milliliters?