Consider the following hypothesis test: Ho: >20 A sample of 55 provided a sample
ID: 3069196 • Letter: C
Question
Consider the following hypothesis test: Ho: >20 A sample of 55 provided a sample mean of 19.6. The population standard deviation is 2. a. Compute the value of the test statistic (to 2 decimals). Enter negative value as negative number. b. What is the p-value (to 3 decimals)? c. Using a 0.05, can it be concluded that the population mean is less than 20? -Select your answer istie (t0 , decima s), Enter negative value as negative number. State the rejection rule: Reject Ho if z is - Select your answer the critical value. Using -0.05, can it be concluded that the population mean is less than 20? 1 -Select your answer-Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: u > 20.0
Alternative hypothesis: u < 20.0
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 0.26968
DF = n - 1
D.F = 54
t = (x - u) / SE
t = - 1.48
tcritical = - 1.674
where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a t statistic test statistic of - 1.48.
Thus the P-value in this analysis is 0.072.
Interpret results. Since the P-value (0.072) is greater than the significance level (0.05), we cannot reject the null hypothesis.
From the above test we cannot conclude that the propulation mean is less than 20.
t = - 1.48
tcritical = - 1.674
where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a t statistic test statistic of - 1.48.
Interpret results. Since the t-value (1.48) is greater than the critucal value(-1.674), we cannot reject the null hypothesis.
From the above test we cannot conclude that the propulation mean is less than 20.
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