Question

The length of human pregnancy is known to have a mean of 266 days and a standard deviation of 16 days. Based on records from a large women's hospital, a random sample of 25 women who were smoking and/or drinking alcohol during their pregnancy and their pregnancy lengths are recorded in the datafile linked below. Do the data provide enough evidence to support the (well-known) fact that women who smoke and/or drink alcohol during their pregnancy have shorter pregnancies than women in general (in other words, are more likely to have premature labor)?

Pregnancy Length (days)
256
276
252
271
239
302
249
246
229
228
235
267
293
249
270
294
260
258
250
242
282
283
237
257
267
1) State the null and alternative hypotheses, and define clearly what the parameter μ represents.
2) Have the conditions that allow us to safely use the z-test been met? support your answer
3) Compute the test statistic and interpret its value
4) State the p-value, and draw your conclusions in context.

Answer 1

H0: μ ≥ 266

H1 : μ < 266

Yes, condition for Ztest have been met.

-1.975

Explanation:

Given that:

μ = 266

Sample size, n = 25

Sample mean, x = 259.68

The Null hypothesis, H0: μ ≥ 266

The Alternative hypothesis, H1 : μ < 266

The test statistic, :

(x - μ) ÷ (s/sqrt(n)

(259.68 - 266) ÷ (16/sqrt(25))

−6.32 / 3.2

= - 1.975

Using the Pvalue from Zstatistic calculator :

Pvalue, one tail test at 0.05, Zscore = - 1.975

Pvalue = 0.024134

Since ;

Pvalue < α ; reject Null

0.024 < 0.05 ;

The is significant evidence to support the claim that women who smoke during their pregnancy have shorter pregnancy than general women.