Question

1- A random sample of 10 students contains the following observations, in hours, for time spent studying in the week before final exams: 28, 57, 42, 35, 61, 39, 55, 46, 49, 38. Assume that the population distribution is normal. Test at the 5% significance level the null hypothesis that the population mean is 40 hours against the alternative that it is higher. (NOTE: We need to assume that class sizes are normally distributed in order to use the t distribution because the sample size n=10 < 25, and the Central Limit Theorem does not apply.) A. Since the test statistic equals 1.50, and the critical t value is 1.833, we fail to reject the null hypothesis and conclude that there is not enough evidence to determine that hours of work is truly higher than 40 hours/week. B. Since the test statistic equals 1.83, and the critical t value is 1.50, we reject the null hypothesis and conclude that there is enough evidence to determine that hours of work is higher than 40 hours/week. C. Since the test statistic equals 1.50, and the critical t value is 2.262, we fail to reject the null hypothesis and conclude that there is not enough evidence to determine that hours of work is truly higher than 40 hours/week. D. Since the test statistic equals 1.50, and the critical t value is 1.812, we fail to reject the null hypothesis and conclude that there is not enough evidence to determine that hours of work is truly higher than 40 hours/week. 2- Screws Inc. has asked for assistance in determining whether the manufacturing process is operating correctly. When the process is operating properly, it produces screws whose weights are normally distributed with a population mean of 5 grams and a population standard deviation of 0.1 grams. The manager wishes to know if the recent change to a new materials supplier has lowered the weight of the screws. In a random sample of 16 screws, the sample mean weight is 4.962 grams. Is there evidence to conclude that lower weight screws are now being produced at a significance level of 5%? The p-value is _______. What is your conclusion?

          1-
A random sample of 10 students contains the following
observations, in hours, for time spent studying in the week before
final exams: 28, 57, 42, 35, 61, 39, 55, 46, 49, 38. Assume that
the population distribution is normal. Test at the 5% significance
level the null hypothesis that the population mean is 40 hours
against the alternative that it is higher. (NOTE: We need to assume
that class sizes are normally distributed in order to use the t
distribution because the sample size n=10 < 25, and the Central
Limit Theorem does not apply.)
A. Since the test statistic equals 1.50, and the critical t
value is 1.833, we fail to reject the null hypothesis and conclude
that there is not enough evidence to determine that hours of work
is truly higher than 40 hours/week.
B. Since the test statistic equals 1.83, and the critical t
value is 1.50, we reject the null hypothesis and conclude that
there is enough evidence to determine that hours of work is higher
than 40 hours/week.
C. Since the test statistic equals 1.50, and the critical t
value is 2.262, we fail to reject the null hypothesis and conclude
that there is not enough evidence to determine that hours of work
is truly higher than 40 hours/week.
D. Since the test statistic equals 1.50, and the critical t
value is 1.812, we fail to reject the null hypothesis and conclude
that there is not enough evidence to determine that hours of work
is truly higher than 40 hours/week.
2-
Screws Inc. has asked for assistance in determining whether the
manufacturing process is operating correctly. When the process is
operating properly, it produces screws whose weights are normally
distributed with a population mean of 5 grams and a population
standard deviation of 0.1 grams. The manager wishes to know if the
recent change to a new materials supplier has lowered the weight of
the screws. In a random sample of 16 screws, the sample mean weight
is 4.962 grams. Is there evidence to conclude that lower weight
screws are now being produced at a significance level of 5%? The
p-value is _______. What is your conclusion?

Added by Luisa W.

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