The average length of a pregnancy (ending in spontaneous labor) is approximately

Question

The average length of a pregnancy (ending in spontaneous labor) is approximately 278 days, but some believe that the arrival time of the first birth tends to be longer. You wish to conduct a hypothesis test to investigate this claim. 1.a) State the null and alternative hypotheses in both words and mathematical notation, to answer the question, "Are first pregnancies generally longer than subsequent ones?" 1.b) You take a SRS of 23 relevant pregnancies and find that they last an average of x=2S0.S days with a sample standard deviation of s = 8.2 days. Calculate a 90% Confidence Interval for the true average. 1.c) Calculate a test statistic for testing the hypothesis in 1.a with the data found in 1.b. 1.d) Based on your test statistic found in 1.e. what is the p-value associated with this test? 1.e) Based on the p-value found in 1.d, testing at a 5% level, what do you conclude about your null and alternative hypotheses? What does this mean in terms of the original question of interest?

Explanation / Answer

Part-a

Null hypothesis H0: =278

Alternative hypothesis H0: >278

Part-b

Degree of freedom=23-1=22

Critical t=1.7171

90% confidence interval =xbar±t*s/sqrt(n)

=280.8±2.7171*8.2/sqrt(23)

=(276.154253        285.445747)

Part-c

Test statistic t=( xbar-278)/(s/sqrt(n))

=(280.8-278)/(8.2/sqrt(23))

=1.6376

Part-d

p-value=0.0579

Part-e

As p-value>0.05, we do not reject the null hypothesis and conclude that arrival time is no longer than 278 days

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