a sample of 16 cookies . Based on the information, answer Question 6 to 9 below.
ID: 3312252 • Letter: A
Question
a sample of 16 cookies . Based on the information, answer Question 6 to 9 below. taken to test the claim that each cookie contains at least 9 chocolate chips. cookie in the sample was 7.875. The standard deviation of The average number of chocolate chips per the number 6. The test statistic is: a.1.96 b. -2.25 c. 2.00 d. -0.50 12. Assume the distribution of the population is normal. Let denote the average of chocolate chips in all the cookies. The hypothesis to test the claim is: Ho: 29 ,ia·9" 7. The critical value for this test at a .0S level of significance is: a. 1.96 b. 1.28 d. 1.645 8· The p-value for this test statistics is: a. 0.0139 b. 0.9878 c. 0.0244 d. 0.0122 At a.05 level of significance, it can be concluded that the mean of the population is significantly less than 9 not significantly less than 9 significantly greater than9 significantly greater than 2.25Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: > 9
Alternative hypothesis: < 9
Note that these hypotheses constitute a one-tailed test.
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 = 0.50
DF = n - 1
D.F = 15
6)
t = (x - ) / SE
t = - 2.25
7)
tcritical = - 2.131
Rejection region is t < - 2.131.
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a t statistic test statistic of - 2.25.
8) Thus the P-value in this analysis is 0.0199
Interpret results. Since the P-value (0.019) is less than the significance level (0.05), we have to reject the null hypothesis.
9) From the above test we can conclude that mean of the population is significantly less than 9.
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