Question

The prices (in dollars) for a graphing calculator are shown below for 8 online vendors.

121 125 151 129 127 133 121 125

(1) Estimate the true mean price for this particular calculator with 95% confidence.

(2) Test at α = 0.05 to see if the mean price for this particular calculator is higher than $122.

Answer 1

1)
sample mean, xbar = 129
sample standard deviation, s = 9.7395
sample size, n = 8
degrees of freedom, df = n - 1 = 7

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.365

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (129 - 2.365 * 9.7395/sqrt(8) , 129 + 2.365 * 9.7395/sqrt(8))
CI = (120.86 , 137.14)

2)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 122
Alternative Hypothesis, Ha: μ > 122

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (129 - 122)/(9.7395/sqrt(8))
t = 2.033

P-value Approach
P-value = 0.0408
As P-value < 0.05, reject the null hypothesis.

There is sufficient evidence to conclude that the mean price for this calculator is greater than 122