Calculate a 99% confidence interval for the population mean height after one week of pea plants that were given 1 ml of growth serum. Interpret the confidence interval.

A botanist was conducting a study on the effects of a special growth serum on pea plants. In particular, they were comparing how different amounts of growth serum (1, 2, 3, 4, 5 and 6 ml) might affect growth. For each amount of growth serum, six pea plant seeds were randomly selected and each seed was given that amount of growth serum. After one week, the height (in cm) of each pea plant that grew from the seed was recorded. Some sample statistics are displayed in the table below. Assume the height of pea plants after one week is normally distributed, regardless of the amount of growth serum given. Growth Serum Sum of Sample Values Sum of Squared Sample Values TEEN23W 2 ml 22;. 13. = 32.7 23;. Y; = 179.71 3 ml 23:1 Y5. = 35.4 2:; 133 = 211.88 4 ml 3;. K..- = 39.6 3;. 7:3 = 261.98 5 1111 23:1 Y5. = 41.7 23;. 7;: = 290.45 6 ml 23:! Y6..- = 44.7 23:! Y; = 335.13