Question

Recorded here are the germination times (in days) for sixteen randomly chosen seeds of a new type of bean: 11, 13, 12, 13, 20, 15, 18, 17, 14, 18, 10, 12, 13, 17, 14, 17 Send data to Excel Assuming that germination times are normally distributed, find a 95% confidence interval for the mean germination time for all beans of this type. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.) What is the lower limit of the confidence interval? What is the upper limit of the confidence interval?

Answer 1

necessary calculation table :-

days (x)	x2
11	121
13	169
12	144
13	169
20	400
15	225
18	324
17	289
14	196
18	324
10	100
12	144
13	169
17	289
14	196
17	289
sum=234	sum=3548

sample size (n) = 16

df = (n-1 )= (16-1) = 15

t critical value for 95% confidence level,df=15 , both tailed test be:-

(using t distribution table)

the 95% confidence interval for the mean germination time for all beans of this type is:-

the lower limit of the confidence interval = 13.1

the upper limit of the confidence interval = 16.2

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