Answer:
a) This t-value obtained (2.92) is in the rejection region (t > 1.69), hence, the sample does not support the cofdee industry's claim.
b) p-value for this test = 0.006266
c) The p-value obtained for this test is lesser than the significance level at which the test was performed, hence, we can reject the nuĺl hypothesis and say that there is enough evidence to suggest that the coffee industry's claim isn't true based in results obtained from the sample data.
Explanation:
a) Degree of freedom = n - 1 = 34 - 1 = 33
The critical value of t for a significance level of 0.10 and degree of freedom of 33 = 1.69
Since we are testing in both directions whether the the average U.S. adult drinks 1.7 cups of coffee per day using our sample,
The rejection region is t < -1.69 and t > 1.69
So, we compute the t-statistic for this sample data to test the claim.
t = (x - μ)/σₓ
x = sample mean = 1.95 cups of coffee per day
μ₀ = The standard we are comparing against = 1.7 cups of coffee per day
σₓ = standard error = (σ/√n)
σ = standard deviation = 0.5 cups
n = Sample size = 34
σₓ = (0.5/√34) = 0.0857492926 = 0.08575
t = (1.95 - 1.70) ÷ 0.08575
t = 2.9154759464 = 2.92
This t-value obtained is in the rejection region, hence, the sample does not support the cofdee industry's claim.
b) Checking the tables for the p-value of this t-statistic
Degree of freedom = df = n - 1 = 34 - 1 = 33
Significance level = 0.10
The hypothesis test uses a two-tailed condition because we're testing in both directions.
p-value (for t = 2.92, at 0.10 significance level, df = 33, with a two tailed condition) = 0.006266
c) To use PHStat, the claim that the average U.S. adult drinks 1.7 cups of coffee per day is the null hypothesis.
The alternative hypothesis is that the real number of cups of coffee that the average U.S. adult drinks as obtained from the sample data, is significantly different from the 1.7 in the coffee industry's claim.
The p-value obtained from PHstat = 0.0063
The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.10
p-value = 0.0063
0.0063 < 0.10
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to suggest that the coffee industry's claim isn't true based in results obtained from the sample data.
Hope this Helps!!!