Recorded here are the germination times (in days) for ten randomly chosen seeds of a new type of bean. See Attached Excel for Data. Assume that the population germination time is normally distributed. Find the 97% confidence interval for the mean germination time.

97% Confidence interval = (12.62, 18.98)

Step-by-step explanation:

Complete Question

Recorded here are the germination times (in days) for ten randomly chosen seeds of a new type of bean: 18, 12, 20, 17, 14, 15, 13, 11, 21, 17. Assume that the population germination time is normally distributed. Find the 97% confidence interval for the mean germination time.

Solution

We first compute the sample mean and standard deviation for this sample distribution

Sample mean = (Σx)/N = (158/10) = 15.8

Standard deviation = √{[Σ(x - xbar)²]/(N-1)} = 3.3598941782278 = 3.36

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Sample Mean = 15.8

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the t-distribution. This is because there is no information provided for the population mean and standard deviation.

To find the critical value from the t-tables, we first find the degree of freedom and the significance level.

Degree of freedom = df = n - 1 = 10 - 1 = 9

Significance level for 97% confidence interval

(100% - 97%)/2 = 1.5% = 0.015

t (0.015, 9) = 2.9982 (from the t-tables)

Standard error of the mean = σₓ = (σ/√n)

σ = standard deviation of the sample = 3.36

n = sample size = 10

σₓ = (3.36/√10) = 1.0625

97% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 15.8 ± (2.9982 × 1.0625)

CI = 15.8 ± 3.1809882246

97% CI = (12.6190117754, 18.9809882246)

97% Confidence interval = (12.62, 18.98)

Hope this Helps!!!

answer: idk

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