Question

4) Given the following hypothesis:
Ho: = 480
H1: = 480

A random sample of 14 observations is selected from a normal population. The sample mean was 488 and the sample standard deviation 8. Using the 0.10 significance level

    a) State the decision rule. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places)

    Reject HO when the test statistic is ____ the interval (__ , ___)

    b) Compute the value of the test statistic.

    Value of the test statistic ______

    c) What is your decision regarding the null hypothesis?
     ___ Reject
     ___ Do not reject

5) The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 1.56 liters. a health campaign promotes the consumption of at least 2.0 liters per day. A sample of 10 adults after the campaign shows the following consumption in liters:

1.88     1.74     1.98     1.70     1.86     1.72     1.74     1.98     1.68     1.50

At the 0.025 significance level, can we conclude that water consumption has increased? Interpret the p-value.

    a) State the null hypothesis and the alternate hypothesis.

    b) State the decision rule for 0.025 significance level. (Round your answer 3 decimal places)   
    
    Reject HO if t > ____  

    

    c) Compute the value of the test statistic. (Round your intermediate and final answer to 3 decimal places)

    Value of the test statistic _______

    d) State the decision rule for 0.025 significance level. (Round your answer to 3 decimal places)

    reject HO if t > _____

6) A sample of 40 observations is selected from a normal population. The sample mean is 31, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.05 significance level.

    a) Is this a one or two- tailed test?

    b) What is the decision rule? (Round your answer 2 decimal places)

    _____ HO, when z > ______

    c) What is the value of the test statistic?

    Value of the test statistic ______

    d) What is your decision regarding Ho?

    ___ Do not reject
    ___ Reject

    There is ____ evidence to conclude that the population mean is greater than 30.

    e) What is the p-value? (Round your answer to 4 decimal places)

    p-value _______

7) A recent national survey found that high school students watched an average (mean) of 7.1 movies per month with a population standard deviation of 1.0. The distribution of number of movies watcher per month follows the normal distribution. A random sample of 41 college students revealed that the mean number of movies watched last month was 6.6. At the 0.05 significance level, can we conclude that college students watch fewer movies a month than high school students?

    a) State the null hypothesis and the alternate hypothesis.

    b) State the decision rule.

    c) Compute the value of the test statistic (negative amount should be indicated by a minus sign. Round your answer 2 decimal places)

    Value of the test statistics ___

    d) What is your decision regarding Ho?

    ___ Reject Ho
   ___ Do not reject Ho

    e) What is the P-value? (Round your answer to 4 decimal places)

8) At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, "You can average $85 a day in tips." Assume the population of daily tips is normally distributed with a standard deviation of $4.50. Over the first 47 days she was employed at the restaurant, the mean daily amount of her tips was $86.06. At the 0.01 significance level, can Ms. Brigden conclude that he daily tips average more than $85.

    a) State the null hypothesis and the alternate hypothesis.

    b) State the decision rule.

    c) Compute the value of the test statistic.

    Value of the test statistic _____

    d) What is your decision regarding Ho?
    ____ Reject Ho
    ____ Do not reject Ho

    e) What is the p-value?

9) The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 38 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 44 sales representatives reveals that the mean number of calls made last week was 40. the standard deviation of the sample is 1.8 calls. Using the 0.100 significance level, can we conclude that the mean number of calls per salesperson in a week is more than 38?

    a) Compute the value of the test statistic (Round your answer to 3 decimal places)

    b) What is your decision regarding Ho?

     ____ Ho. The mean number of calls is ____ that 38 per week.

10) The mean income per perso in the United States is $44,000, and the distribution of incomes follows a normal distribution. A random sample of 15 residents of Wilmington, Delaware, had a mean of $48,000 with a standard deviation of $10,500. At the 0.100 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income that the national average?

    a) State the null hypothesis and the alternate hypothesis.

    b) State the decision rule for 0.100 significance level (Round your answer to 3 decimal places)

    c) Compute the value of the test statistic. (Round your answer to 2 decimal places)

    d) Is there enough evidence to substantiate that residents of Wilmington, Delaware, have more income than       
         the national average at the 0.100 significance level?

    ___ Ho. There is ____ evidence to conclude that the mean income in Wilmington is ____ 44000.

Answer 1

Solution:

Question 4)

We are given the following hypothesis:

vs

Sample size = n = 14

Sample mean =

Sample standard deviation = s = 8

significance level =

Part a) State the decision rule.

Since is not equal to type, this is two tailed test.

df = n - 1 = 14 - 1 = 13

Two tail area =

Look in t table for df = 13 and two tail area = and find corresponding t critical value.

This is two tailed test , so we have two critical values

thus t critical values are: ( -1.771 , 1.771)

Thus decision rule is:   Reject H₀ when the test statistic is outside the interval ( -1.771 , 1.771 )

Part b) Compute the value of the test statistic.

Part c) What is your decision regarding the null hypothesis?

Since t = 3.742 > 1.771 , that is t test statistic fall outside the range of critical values, we reject null hypothesis H0.

Thus correct option is we reject H0.