The UMUC bookstore states the average textbook costs $119. A randomly selected sample of 26 new textbooks at the UMUC bookstore had a mean price of $123.45 and sample standard deviation of $15.23. Use a 0.05 significance level to test the claim that the mean price of textbooks at the UMUC bookstore is significantly more than $119 (use the p-value method). Show your work.

Question

The UMUC bookstore states the average textbook costs $119. A randomly selected sample of 26 new textbooks at the UMUC bookstore had a mean price of $123.45 and sample standard deviation of $15.23. Use a 0.05 significance level to test the claim that the mean price of textbooks at the UMUC bookstore is significantly more than $119 (use the p-value method). Show your work.

a. Give the symbolic null & alternative hypotheses. Use proper notation.
H0: HA:
b. Determine the test statistic (round to 3 decimal places):
c. Determine the p-value (round to 3 decimal places):
d. Result (Circle one & justify): REJECT 𝑯𝟎 FAIL TO REJECT 𝑯𝟎
Reason:
e. State a conclusion within the context of the scenario:

Can someone please check my work.

a. H0: µ ≤ 119
HA: µ > 119

b. Test statistic = (123.45-119)/15.22/√26 = 1.490

c. df = 26-1 = 25
This is a right tailed test.
P value = P(t(25) > 1.490)= 0.074

d. Fail to reject Ho
Reason: the p value of 0.074 is larger than significance level of 0.05

e. We do not reject the null hypothesis due to the data not providing enough evidence that the population mean price of textbooks at the umuc bookstore is more than $119.

Answer 1

Your work appears to be correct. Let's go through each step to verify:

a. The null hypothesis (H0) states that the mean price of textbooks at the UMUC bookstore is less than or equal to $119. The alternative hypothesis (HA) states that the mean price is greater than $119.

b. To calculate the test statistic, you used the formula:

(test statistic) = (sample mean - population mean) / (sample standard deviation / √(sample size)).

In this case, the sample mean is $123.45, the population mean is $119, sample standard deviation is $15.23, and the sample size is 26. Plugging in these values, you correctly found the test statistic to be 1.490 (rounded to 3 decimal places).

c. The degrees of freedom (df) is equal to the sample size minus 1, which is 26 - 1 = 25. Since this is a right-tailed test, we want to find the probability that the t-distribution is greater than the test statistic. Using a t-table or calculator, you determined the p-value to be 0.074 (rounded to 3 decimal places).

d. Since the p-value of 0.074 is greater than the significance level of 0.05, we fail to reject the null hypothesis (Ho).

e. In the context of the scenario, the conclusion is that there is not enough evidence to support the claim that the mean price of textbooks at the UMUC bookstore is significantly more than $119.

Overall, your work is correct. Good job!