Question

Problem 4: A high submarine heater must shut down if the average temperature arises to 7.5C°. Before the shut down black box of the submarine records the temperature. The results of 10 recordings are the following: | 7.54 | 7.44 7.40 7.43 7.36 7.34 7.61 7.39 7.51 7.45 If the temperature has normal distribution and x = 74.47,0 = 0.08. a) State a hypothesis to test if the data suggests, that the heater shuts down too early? [5 points] b) Test the hypothesis with significance level of a = 0.05, use z-value approach. [10 points] c) What can we conclude? Shall the submarine be repaired? [5 points)

Answer 1

a)

Xbar = 74.47/10 = 7.447

z-value based Population MEAN Hypothesis Test xbar = sample mean = standard deviation = n = sample size = a = alpha = 7.4470 0.0800 10 0.05 Step 1: State Ho and Ha Population parameter comparison value? Is this a LEFT, RIGHT or TWO tailed test? 7.5 LEFT-tailed Null Hypothesis: Alternate Hypothesis: Ho: u 27.5 Ha: u < 7.5 Step 2: State Decision Criteria; Find Critical Values Reject Ho if z< -1.645 or Reject Ho if p-value <a = 0.05 Step 3: Calculate Test Statistic Test statistic = z = p-value = -2.0950 0.0181 Step 4: Make Decision Reject Ho Reject Ho since p-value (0.0181) IS less than a, alpha, = 0.05. Also, we Reject Ho since the Test statistic (-2.09501) meets the rejection criteria in STEP 2. Step 5: Summarize Decision There is sufficient statistical evidence to reject Ho.

c)

since we reject the null hypothesis, heater shuts down too early.

submarine should be repaired

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