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Question 16 4 pts Test the indicated daim about the means of two populations. Assume that the two samples are independent simple random samples selected from normally distributed populations Two types of flares are tested and their burning times in minutes are recorded. The summary statistics are given below. Use any method to determine if there is a significant difference in the burning times of the flares using a significance level of 0.05. Beady Brand X n-1 40 1-0 min No there is not a statistically significant difference Yes there is a statistically significant difference D Question 17 4 pts A researcher was interested in comparing the amount of time spent watching television by women and by men. Independent simple random samples of 14 women and 17 men were selected, and each person was asked how many hours he or she had watched television during the previous week. The summary statistics are shown in the chart below. The following 99% confidence interval was obtained for the difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for ment -5.73 hrs <ul-2413 hrs. What does the condence interval suggest about the population means? Women *i- 157 2-19-52 lus - 14 Men 17 The confidence intervalimits includeo which suggests that the two population means are unlikely to be coul. There appears to be asicant difference between the sount of time spent watching television for women and the mean amount of timespert watching television for men The conhdence interval includes only negative values which sugests that the mean amount of time spent watching te vor for women's smaller than the meanaount of time spent watching television for men The confidence intervalimits include which suggests that the two population means might be there does not apear to be picant difference between the mean amount of time watching te voor watten and then an amount of time see watching television for men The condence intervalindudes only positive values which suggests that the mean amount of time spent watching television for women arer than the mean amount of time watching television for men

Answer 1

16)

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: M1 = M2 Ha: M1 7 M2 This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the degrees of freedom are df = 52.47. In fact, the degrees of freedom are computed as follows, assuming that the population variances are unequal: 2.006, for Hence, it is found that the critical value for this two-tailed test is te 0.05 and df = 52.47. a = The rejection region for this two-tailed test is R = {t:\t> 2.006). : (3) Test Statistics Since it is assumed that the population variances are unequal, the t-statistic is computed as follows: t= Žj - X2 로 ni n2 19.4 – 15.1 16.025 1.42 V 35 + 0.82 40 (4) Decision about the null hypothesis Since it is observed that t1 = 16.025 > tc = 2.006, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p = 0, and since p= 0 < 0.05, it is concluded that the null hypothesis is rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean Mi is different than 42, at the 0.05 significance level.

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