Slove the following exponential decay function for t when x= 5. Round to the nearest hundredth.
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Answer:
Step-by-step explanation:
Given that:
population mean = 25
sample size = 50
sample mean = 24.02
standard deviation = 4.75
The null and alternative hypothesis can be computed as follows:
Null hypothesis:
Alternative hypothesis:
b. Yes, the necessary assumptions to perform the inference are satisfied because the sample size is large and as a result, the data approximately follows a normal distribution.
c. To determine the P-value, we need to Find the t-test statistics which can be expressed by the formula:
t = - 1.458
The degree of freedom df = n- 1 = 50 - 1 = 49
The p -value = P(T < -1.458)
p -value = 0.0756
d. The p-value is the probability of finding the observed value when null hypothesis is true.
e.
Decision rule: To reject the null hypothesis if the level of significance at 0.05 is greater than the p-value.
Conclusion: We fail to reject the null hypothesis because the p-value is greater than the level of significance, hence, there is no sufficient evidence to conclude that the company has failed to meet its goal.